15.2: Bureaucracy and the Evolution of Public Administration
-
- Last updated
- Save as PDF
Learning Objectives
By the end of this section, you will be able to:
- Define bureaucracy and bureaucrat
- Describe the evolution and growth of public administration in the United States
- Identify the reasons people undertake civil service
Throughout history, both small and large nations have elevated certain types of nonelected workers to positions of relative power within the governmental structure. Collectively, these essential workers are called the bureaucracy. A bureaucracy is an administrative group of nonelected officials charged with carrying out functions connected to a series of policies and programs. In the United States, the bureaucracy began as a very small collection of individuals. Over time, however, it grew to be a major force in political affairs. Indeed, it grew so large that politicians in modern times have ridiculed it to great political advantage. However, the country’s many bureaucrats or civil servants, the individuals who work in the bureaucracy, fill necessary and even instrumental roles in every area of government: from high-level positions in foreign affairs and intelligence collection agencies to clerks and staff in the smallest regulatory agencies. They are hired, or sometimes appointed, for their expertise in carrying out the functions and programs of the government.
What does a Bureaucracy do?
Modern society relies on the effective functioning of government to provide public goods, enhance quality of life, and stimulate economic growth. The activities by which government achieves these functions include—but are not limited to—taxation, homeland security, immigration, foreign affairs, and education. The more society grows and the need for government services expands, the more challenging bureaucratic management and public administration becomes. Public administration is both the implementation of public policy in government bureaucracies and the academic study that prepares civil servants for work in those organizations.
The classic version of a bureaucracy is hierarchical and can be described by an organizational chart that outlines the separation of tasks and worker specialization while also establishing a clear unity of command by assigning each employee to only one boss. Moreover, the classic bureaucracy employs a division of labor under which work is separated into smaller tasks assigned to different people or groups. Given this definition, bureaucracy is not unique to government but is also found in the private and nonprofit sectors. That is, almost all organizations are bureaucratic regardless of their scope and size; although public and private organizations differ in some important ways. For example, while private organizations are responsible to a superior authority such as an owner, board of directors, or shareholders, federal governmental organizations answer equally to the president, Congress, the courts, and ultimately the public. The underlying goals of private and public organizations also differ. While private organizations seek to survive by controlling costs, increasing market share, and realizing a profit, public organizations find it more difficult to measure the elusive goal of operating with efficiency and effectiveness.
Link to Learning
To learn more about the practice of public administration and opportunities to get involved in your local community, explore the American Society for Public Administration website.
Bureaucracy may seem like a modern invention, but bureaucrats have served in governments for nearly as long as governments have existed. Archaeologists and historians point to the sometimes elaborate bureaucratic systems of the ancient world, from the Egyptian scribes who recorded inventories to the biblical tax collectors who kept the wheels of government well greased. 1 In Europe, government bureaucracy and its study emerged before democracies did. In contrast, in the United States, a democracy and the Constitution came first, followed by the development of national governmental organizations as needed, and then finally the study of U.S. government bureaucracies and public administration emerged. 2
In fact, the long pedigree of bureaucracy is an enduring testament to the necessity of administrative organization. More recently, modern bureaucratic management emerged in the eighteenth century from Scottish economist Adam Smith’s support for the efficiency of the division of labor and from Welsh reformer Robert Owen’s belief that employees are vital instruments in the functioning of an organization. However, it was not until the mid-1800s that the German scholar Lorenz von Stein argued for public administration as both a theory and a practice since its knowledge is generated and evaluated through the process of gathering evidence. For example, a public administration scholar might gather data to see whether the timing of tax collection during a particular season might lead to higher compliance or returns. Credited with being the father of the science of public administration, von Stein opened the path of administrative enlightenment for other scholars in industrialized nations.
The Origins of the U.S. Bureaucracy
In the early U.S. republic, the bureaucracy was quite small. This is understandable since the American Revolution was largely a revolt against executive power and the British imperial administrative order. Nevertheless, while neither the word “bureaucracy” nor its synonyms appear in the text of the Constitution, the document does establish a few broad channels through which the emerging government could develop the necessary bureaucratic administration.
For example, Article II, Section 2, provides the president the power to appoint officers and department heads. In the following section, the president is further empowered to see that the laws are “faithfully executed.” More specifically, Article I, Section 8, empowers Congress to establish a post office, build roads, regulate commerce, coin money, and regulate the value of money. Granting the president and Congress such responsibilities appears to anticipate a bureaucracy of some size. Yet the design of the bureaucracy is not described, and it does not occupy its own section of the Constitution as bureaucracy often does in other countries’ governing documents; the design and form were left to be established in practice.
Under President George Washington, the bureaucracy remained small enough to accomplish only the necessary tasks at hand. 3 Washington’s tenure saw the creation of the Department of State to oversee international issues, the Department of the Treasury to control coinage, and the Department of War to administer the armed forces. The employees within these three departments, in addition to the growing postal service, constituted the major portion of the federal bureaucracy for the first three decades of the republic (Figure 15.2). Two developments, however, contributed to the growth of the bureaucracy well beyond these humble beginnings.
The first development was the rise of centralized party politics in the 1820s. Under President Andrew Jackson, many thousands of party loyalists filled the ranks of the bureaucratic offices around the country. This was the beginning of the spoils system, in which political appointments were transformed into political patronage doled out by the president on the basis of party loyalty. 4 Political patronage is the use of state resources to reward individuals for their political support. The term “spoils” here refers to paid positions in the U.S. government. As the saying goes, “to the victor,” in this case the incoming president, “go the spoils.” It was assumed that government would work far more efficiently if the key federal posts were occupied by those already supportive of the president and his policies. This system served to enforce party loyalty by tying the livelihoods of the party faithful to the success or failure of the party. The number of federal posts the president sought to use as appropriate rewards for supporters swelled over the following decades.
The second development was industrialization, which in the late nineteenth century significantly increased both the population and economic size of the United States. These changes in turn brought about urban growth in a number of places across the East and Midwest. Railroads and telegraph lines drew the country together and increased the potential for federal centralization. The government and its bureaucracy were closely involved in creating concessions for and providing land to the western railways stretching across the plains and beyond the Rocky Mountains. These changes set the groundwork for the regulatory framework that emerged in the early twentieth century.
The Fall of Political Patronage
Patronage had the advantage of putting political loyalty to work by making the government quite responsive to the electorate and keeping election turnout robust because so much was at stake. However, the spoils system also had a number of obvious disadvantages. It was a reciprocal system. Clients who wanted positions in the civil service pledged their political loyalty to a particular patron who then provided them with their desired positions. These arrangements directed the power and resources of government toward perpetuating the reward system. They replaced the system that early presidents like Thomas Jefferson had fostered, in which the country’s intellectual and economic elite rose to the highest levels of the federal bureaucracy based on their relative merit. 5 Criticism of the spoils system grew, especially in the mid-1870s, after numerous scandals rocked the administration of President Ulysses S. Grant (Figure 15.3).
As the negative aspects of political patronage continued to infect bureaucracy in the late nineteenth century, calls for civil service reform grew louder. Those supporting the patronage system held that their positions were well earned; those who condemned it argued that federal legislation was needed to ensure jobs were awarded on the basis of merit. Eventually, after President James Garfield had been assassinated by a disappointed office seeker (Figure 15.4), Congress responded to cries for reform with the Pendleton Act, also called the Civil Service Reform Act of 1883. The act established the Civil Service Commission, a centralized agency charged with ensuring that the federal government’s selection, retention, and promotion practices were based on open, competitive examinations in a merit system. 6 The passage of this law sparked a period of social activism and political reform that continued well into the twentieth century.
As an active member and leader of the Progressive movement, President Woodrow Wilson is often considered the father of U.S. public administration. Born in Virginia and educated in history and political science at Johns Hopkins University, Wilson became a respected intellectual in his fields with an interest in public service and a profound sense of moralism. He was named president of Princeton University, became president of the American Political Science Association, was elected governor of New Jersey, and finally was elected the twenty-eighth president of the United States in 1912.
Wilson advocated separating politics from administration by three key means: making comparative analyses of public and private organizations, improving efficiency with business-like practices, and increasing effectiveness through management and training. Wilson’s point was that while politics should be kept separate from administration, administration should not be insensitive to public opinion. Rather, the bureaucracy should act with a sense of vigor to understand and appreciate public opinion. Still, Wilson acknowledged that the separation of politics from administration was an ideal and not necessarily an achievable reality.
The Bureaucracy comes of Age
The late nineteenth and early twentieth centuries were a time of great bureaucratic growth in the United States: The Interstate Commerce Commission was established in 1887, the Federal Reserve Board in 1913, the Federal Trade Commission in 1914, and the Federal Power Commission in 1920.
Under President Lyndon B. Johnson in the 1960s, that number reached 2.2 million, and the federal budget increased to $332 billion. 10 This growth came as a result of what Johnson called his Great Society program, intended to use the power of government to relieve suffering and accomplish social good. The Economic Opportunity Act of 1964 was designed to help end poverty by creating a Job Corps and a Neighborhood Youth Corps. Volunteers in Service to America was a type of domestic Peace Corps intended to relieve the effects of poverty. Johnson also directed more funding to public education, created Medicare as a national insurance program for the elderly, and raised standards for consumer products.
All of these new programs required bureaucrats to run them, and the national bureaucracy naturally ballooned. Its size became a rallying cry for conservatives, who eventually elected Ronald Reagan president for the express purpose of reducing the bureaucracy. While Reagan was able to work with Congress to reduce some aspects of the federal bureaucracy, he contributed to its expansion in other ways, particularly in his efforts to fight the Cold War. 11 For example, Reagan and Congress increased the defense budget dramatically over the course of the 1980s. 12 After the end of the Cold War and the dismantling of the Berlin Wall, which was an important symbol of East-West conflict during that time, the 1990s brought discussion of a "Peace Dividend"—that is, with the threat of global thermonuclear war significantly reduced, the U.S. could stand to reduce defense spending and direct resources to other areas. 13 However, after a decade of retrenchment in military and defense spending, the 9/11 attacks induced a new era of massive investment in defense and homeland security. Indeed, President Joe Biden's plans to withdraw from Afghanistan come twenty years after the fact. 14
Milestone
“The Nine Most Terrifying Words in the English Language”
The two periods of increased bureaucratic growth in the United States, the 1930s and the 1960s, accomplished far more than expanding the size of government. They transformed politics in ways that continue to shape political debate today. While the bureaucracies created in these two periods served important purposes, many at that time and even now argue that the expansion came with unacceptable costs, particularly economic costs. The common argument that bureaucratic regulation smothers capitalist innovation was especially powerful in the Cold War environment of the 1960s, 70s, and 80s. But as long as voters felt they were benefiting from the bureaucratic expansion, as they typically did, the political winds supported continued growth.
In the 1970s, however, Germany and Japan were thriving economies in positions to compete with U.S. industry. This competition, combined with technological advances and the beginnings of computerization, began to eat away at American prosperity. Factories began to close, wages began to stagnate, inflation climbed, and the future seemed a little less bright. In this environment, tax-paying workers were less likely to support generous welfare programs designed to end poverty. They felt these bureaucratic programs were adding to their misery in order to support unknown others.
In his first and unsuccessful presidential bid in 1976, Ronald Reagan, a skilled politician and governor of California, stoked working-class anxieties by directing voters’ discontent at the bureaucratic dragon he proposed to slay. When he ran again four years later, his criticism of bureaucratic waste in Washington carried him to a landslide victory. While it is debatable whether Reagan actually reduced the size of government, he continued to wield rhetoric about bureaucratic waste to great political advantage. Even as late as 1986, he continued to rail against the Washington bureaucracy (Figure 15.5), once declaring famously that “the nine most terrifying words in the English language are: I’m from the government, and I’m here to help.”
Why might people be more sympathetic to bureaucratic growth during periods of prosperity? In what way do modern politicians continue to stir up popular animosity against bureaucracy to political advantage? Is it effective? Why or why not?


Students and teachers rely on fair use in order to accomplish many of their educational goals. Below are some, but by no means all, educational activities that rely upon fair use.
Student Projects.
Includes both media and text. Your fair use analysis will change depending on how the project is presented, i.e. only the professor sees it, you present it to the whole class, you present it to a group outside of the class, or you post it online for anyone to see.
Course Reserves.
Includes electronic reserves. Instructors may copy or post small portions of books or journals for supplementary student readings, but cannot copy entire copyrighted works as a replacement for materials that students would normally be required to purchase.
Sound or Video Clips for Teaching.
Students and teachers can make use of video or sound clips in creating multi-media presentations for use in the classroom.
Digitization Projects.
Many university libraries rely on fair use in order to create large scale digitization projects that preserve older materials, as well as providing improved access to their collections for the purpose of research. For an example of this type of digitization project check out the
HathiTrust Digital Library
.
Content in Scholarly Articles.
It is common to quote other researchers’ writings or use others’ images, graphs or charts in your own scholarly writing. These practices have long been considered acceptable under fair use.
Access for the Disabled.
When specific exemptions don’t fit. While there are specific exceptions that allow for making copies of copyrighted works in order to provide access to the visually handicapped, they are sometimes too narrow to provide complete access. In these cases it is possible to rely upon fair use in order to provide access to materials.
Fair Use for Non-Educational Purposes.
Fair use is not only available for educational purposes. Many other commercial and non-commercial activities depend upon fair use. Some of these common fair uses include:
-
Quotes in books, news reports and blogs
-
Mash-ups and remixes
-
Parody, such as on television shows like South Park or Saturday Night Live
-
Video or sound clips in documentary films
-
Thumbnail images on search engines
Video Clip: Sesame Street - Gone With the Wind
Check out this parody from Sesame Street.
A YouTube element has been excluded from this version of the text. You can view it online
here
.
Myths About Fair Use
Many people have heard of fair use and have some ideas about what it is. Unfortunately, there are many myths or misunderstandings about exactly what fair use covers, what the law states or how it can be applied. Below we dispel just a few of the most common myths about fair use.
Myth 1: All educational use is fair use.
Fact:
While many educational uses are considered fair use, there are some activities that do not meet the fair use criteria. For example, a teacher can’t make copies of an entire text book so that students don’t have to buy it.
Myth 2: Every educational use is transformative.
Fact:
Using copyrighted works for teaching can often be a transformative use, but not always. For example, using a text book created to teach Biology 101 to teach Biology 101 is not transformative.
Myth 3: All socially beneficial use is fair use.
Fact:
Fair use is designed to help balance the rights of the creator and the social benefit of using copyrighted works in certain ways. Not all uses of copyrighted works that would be socially beneficial, however, qualify as fair use. For example, scanning and posting an entire medical text book online for anyone to access for free is socially beneficial but probably not fair use.
Myth 4: All commercial use precludes fair use.
Fact:
Many commercial activities, such as newspapers and online news sites, rely heavily on fair use.
Myth 5: It is not possible to have a fair use when a permissions scheme exists for a work.
Fact:
Just because rights holders are willing to charge you to use their copyrighted material, does not mean that fair use cannot apply. For example, the Associated Press created a licensing scheme to quote from AP stories but quoting from news stories has long been considered fair use.
Myth 6: Fair use specifies a percentage or amount of a work that is okay to use.
Fact:
The law does not state that using 10% of a book or 30 seconds of a song or video clip is fair use. You can often use more than these arbitrary limits, while sometimes using even less might not be fair use. The amount of the original work used is only one of the four factors to consider.


2.7: Find Multiples and Factors (Part 1)
- Identify multiples of numbers
- Use common divisibility tests
- Find all the factors of a number
- Identify prime and composite numbers
Before you get started, take this readiness quiz.
- Which of the following numbers are counting numbers (natural numbers)? \(0, 4, 215\) If you missed this problem, review Example 1.1.1 .
- Find the sum of \(3\), \(5\), and \(7\). If you missed the problem, review Section 2.1 .
Identify Multiples of Numbers
Annie is counting the shoes in her closet. The shoes are matched in pairs, so she doesn’t have to count each one. She counts by twos: \(2, 4, 6, 8, 10, 12\).
The numbers \(2, 4, 6, 8, 10, 12\) are called multiples of \(2\). Multiples of \(2\) can be written as the product of a counting number and \(2\). The first six multiples of \(2\) are given below.
\[\begin{split} 1 \cdot 2 & = 2 \\ 2 \cdot 2 & = 4 \\ 3 \cdot 2 & = 6 \\ 4 \cdot 2 & = 8 \\ 5 \cdot 2 & = 10 \\ 6 \cdot 2 &= 12 \end{split} \nonumber \]
A multiple of a number is the product of the number and a counting number. So a multiple of \(3\) would be the product of a counting number and \(3\). Below are the first six multiples of \(3\).
\[\begin{split} 1 \cdot 3 & = 3 \\ 2 \cdot 3 & = 6 \\ 3 \cdot 3 & = 9 \\ 4 \cdot 3 & = 12 \\ 5 \cdot 3 & = 15 \\ 6 \cdot 3 &= 18 \end{split} \nonumber \]
We can find the multiples of any number by continuing this process. Table \(\PageIndex{1}\) shows the multiples of \(2\) through \(9\) for the first twelve counting numbers.
| Counting Number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Multiples of 2 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 | 22 | 24 |
| Multiples of 3 | 3 | 6 | 9 | 12 | 15 | 18 | 21 | 24 | 27 | 30 | 33 | 36 |
| Multiples of 4 | 4 | 8 | 12 | 16 | 20 | 24 | 28 | 32 | 36 | 40 | 44 | 48 |
| Multiples of 5 | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 | 60 |
| Multiples of 6 | 6 | 12 | 18 | 24 | 30 | 36 | 42 | 48 | 54 | 60 | 66 | 72 |
| Multiples of 7 | 7 | 14 | 21 | 28 | 35 | 42 | 49 | 56 | 63 | 70 | 77 | 84 |
| Multiples of 8 | 8 | 16 | 24 | 32 | 40 | 48 | 56 | 64 | 72 | 80 | 88 | 96 |
| Multiples of 9 | 9 | 18 | 27 | 36 | 45 | 54 | 63 | 72 | 81 | 90 | 99 | 108 |
A number is a multiple of \(n\) if it is the product of a counting number and \(n\).
Recognizing the patterns for multiples of \(2\), \(5\), \(10\), and \(3\) will be helpful to you as you continue in this course.
Figure \(\PageIndex{1}\) shows the counting numbers from \(1\) to \(50\). Multiples of \(2\) are highlighted. Do you notice a pattern?
Figure \(\PageIndex{1}\): Multiples of 2 between 1 and 50
The last digit of each highlighted number in Figure \(\PageIndex{1}\) is either \(0\), \(2\), \(4\), \(6\), or \(8\). This is true for the product of \(2\) and any counting number. So, to tell if any number is a multiple of \(2\) look at the last digit. If it is \(0\), \(2\), \(4\), \(6\), or \(8\), then the number is a multiple of \(2\).
Determine whether each of the following is a multiple of \(2\):
- \(489\)
- \(3,714\)
Solution
| Is 489 a multiple of 2? | |
| Is the last digit 0, 2, 4, 6, or 8? | No. |
| 489 is not a multiple of 2. |
| Is 3,714 a multiple of 2? | |
| Is the last digit 0, 2, 4, 6, or 8? | Yes. |
| 3,714 is a multiple of 2. |
Determine whether each number is a multiple of \(2\):
- \(678\)
- \(21,493\)
- Answer a
-
yes
- Answer b
-
no
Determine whether each number is a multiple of \(2\):
- \(979\)
- \(17,780\)
- Answer a
-
no
- Answer b
-
yes
Now let’s look at multiples of \(5\). Figure \(\PageIndex{2}\) highlights all of the multiples of \(5\) between \(1\) and \(50\). What do you notice about the multiples of \(5\)?
Figure \(\PageIndex{2}\): Multiples of 5 between 1 and 50
All multiples of \(5\) end with either \(5\) or \(0\). Just like we identify multiples of \(2\) by looking at the last digit, we can identify multiples of \(5\) by looking at the last digit.
Determine whether each of the following is a multiple of \(5\):
- \(579\)
- \(880\)
Solution
| Is 579 a multiple of 5? | |
| Is the last digit 5 or 0? | No. |
| 579 is not a multiple of 5. |
| Is 880 a multiple of 5? | |
| Is the last digit 5 or 0? | Yes. |
| 880 is not a multiple of 5. |
Determine whether each number is a multiple of \(5\).
- \(675\)
- \(1,578\)
- Answer a
-
yes
- Answer b
-
no
Determine whether each number is a multiple of \(5\).
- \(421\)
- \(2,690\)
- Answer a
-
no
- Answer b
-
yes
Figure \(\PageIndex{3}\) highlights the multiples of \(10\) between \(1\) and \(50\). All multiples of \(10\) all end with a zero.
Figure \(\PageIndex{3}\): Multiples of 10 between 1 and 50
Determine whether each of the following is a multiple of \(10\):
- \(425\)
- \(350\)
Solution
| Is 425 a multiple of 10? | |
| Is the last digit zero? | No. |
| 425 is not a multiple of 10. |
| Is 350 a multiple of 10? | |
| Is the last digit zero? | Yes. |
| 350 is a multiple of 10. |
Determine whether each number is a multiple of \(10\):
- \(179\)
- \(3,540\)
- Answer a
-
no
- Answer b
-
yes
Determine whether each number is a multiple of \(10\):
- \(110\)
- \(7,595\)
- Answer a
-
yes
- Answer b
-
no
Figure \(\PageIndex{4}\) highlights multiples of \(3\). The pattern for multiples of \(3\) is not as obvious as the patterns for multiples of \(2\), \(5\), and \(10\).
Figure \(\PageIndex{4}\): Multiples of 3 between 1 and 50
Unlike the other patterns we’ve examined so far, this pattern does not involve the last digit. The pattern for multiples of \(3\) is based on the sum of the digits. If the sum of the digits of a number is a multiple of \(3\), then the number itself is a multiple of \(3\). See Table \(\PageIndex{2}\).
| Multiple of 3 | 3 | 6 | 9 | 12 | 15 | 18 | 21 | 24 |
|---|---|---|---|---|---|---|---|---|
| Sum of digits | 3 | 6 | 9 |
1 + 2 3 |
1 + 5 6 |
1 + 8 9 |
2 + 1 3 |
2 + 4 6 |
Consider the number \(42\). The digits are \(4\) and \(2\), and their sum is \(4 + 2 = 6\). Since \(6\) is a multiple of \(3\), we know that \(42\) is also a multiple of \(3\).
Determine whether each of the given numbers is a multiple of \(3\):
- \(645\)
- \(10,519\)
Solution
- Is \(645\) a multiple of \(3\)?
| Find the sum of the digits. | 6 + 4 + 5 = 15 |
| Is 15 a multiple of 3? | Yes. |
| If we're not sure, we could add its digits to find out. We can check it by dividing 645 by 3. | 645 ÷ 3 |
| The quotient is 215. | 3 • 215 = 645 |
- Is \(10,519\) a multiple of \(3\)?
| Find the sum of the digits. | 1 + 0 + 5 + 1 + 9 = 16 |
| Is 15 a multiple of 3? | No. |
| So 10,519 is not a multiple of 3 either.. | 645 ÷ 3 |
| We can check this by dividing by 10,519 by 3. |
When we divide \(10,519\) by \(3\), we do not get a counting number, so \(10,519\) is not the product of a counting number and \(3\). It is not a multiple of \(3\).
Determine whether each number is a multiple of \(3\):
- \(954\)
- \(3,742\)
- Answer a
-
yes
- Answer b
-
no
Determine whether each number is a multiple of \(3\):
- \(643\)
- \(8,379\)
- Answer a
-
no
- Answer b
-
yes
Look back at the charts where you highlighted the multiples of \(2\), of \(5\), and of \(10\). Notice that the multiples of \(10\) are the numbers that are multiples of both \(2\) and \(5\). That is because \(10 = 2 • 5\). Likewise, since \(6 = 2 • 3\), the multiples of \(6\) are the numbers that are multiples of both \(2\) and \(3\).
Use Common Divisibility Tests
Another way to say that \(375\) is a multiple of \(5\) is to say that \(375\) is divisible by \(5\). In fact, \(375 ÷ 5\) is \(75\), so \(375\) is \(5 • 75\). Notice in Example \(\PageIndex{4}\) that \(10,519\) is not a multiple \(3\). When we divided \(10,519\) by \(3\) we did not get a counting number, so \(10,519\) is not divisible by \(3\).
If a number \(m\) is a multiple of \(n\), then we say that \(m\) is divisible by \(n\).
Since multiplication and division are inverse operations, the patterns of multiples that we found can be used as divisibility tests. Table \(\PageIndex{3}\) summarizes divisibility tests for some of the counting numbers between one and ten.
| A number is divisible by | |
|---|---|
| 2 | if the last digit is 0, 2, 4, 6, or 8 |
| 3 | if the sum of the digits is divisible by 3 |
| 5 | if the last digit is 5 or 0 |
| 6 | if divisible by both 2 and 3 |
| 10 | if the last digit is 0 |
Determine whether \(1,290\) is divisible by \(2\), \(3\), \(5\), and \(10\).
Solution
Table \(\PageIndex{4}\) applies the divisibility tests to \(1,290\). In the far right column, we check the results of the divisibility tests by seeing if the quotient is a whole number.
| Divisible by…? | Test | Divisible? | Check |
|---|---|---|---|
| 2 | Is last digit 0, 2, 4, 6, or 8? | yes | 1290 ÷ 2 = 645 |
| 3 |
Is sum of digits divisible by 3? 1 + 2 + 9 + 0 = 12 |
yes | 1290 ÷ 3 = 430 |
| 5 | Is last digit 5 or 0? | yes | 1290 ÷ 5 = 258 |
| 10 | Is last digit 0? | yes | 1290 ÷ 10 = 129 |
Thus, \(1,290\) is divisible by \(2\), \(3\), \(5\), and \(10\).
Determine whether the given number is divisible by \(2\), \(3\), \(5\), and \(10\).
\(6240\)
- Answer
-
Divisible by \(2\), \(3\), \(5\), and \(10\)
Determine whether the given number is divisible by \(2\), \(3\), \(5\), and \(10\).
\(7248\)
- Answer
-
Divisible by \(2\) and \(3\), not \(5\) or \(10\)
Determine whether \(5,625\) is divisible by \(2\), \(3\), \(5\), and \(10\).
Solution
Table \(\PageIndex{5}\) applies the divisibility tests to \(5,625\) and tests the results by finding the quotients.
| Divisible by…? | Test | Divisible? | Check |
|---|---|---|---|
| 2 | Is last digit 0, 2, 4, 6, or 8? | no | 5625 ÷ 2 = 2812.5 |
| 3 |
Is sum of digits divisible by 3? 5 + 6 + 2 + 5 = 18 |
yes | 5625 ÷ 3 = 1875 |
| 5 | Is last digit 5 or 0? | yes | 5625 ÷ 5 = 1125 |
| 10 | Is last digit 0? | no | 5625 ÷ 10 = 562.5 |
Thus, \(5,625\) is divisible by \(3\) and \(5\), but not \(2\), or \(10\).
Determine whether the given number is divisible by \(2\), \(3\), \(5\), and \(10\).
\(4962\)
- Answer
-
Divisible by \(2\), \(3\), not \(5\) or \(10\)
Determine whether the given number is divisible by \(2\), \(3\), \(5\), and \(10\).
\(3765\)
- Answer
-
Divisible by \(3\) and \(5\)
Find All the Factors of a Number
There are often several ways to talk about the same idea. So far, we’ve seen that if \(m\) is a multiple of \(n\), we can say that \(m\) is divisible by \(n\). We know that \(72\) is the product of \(8\) and \(9\), so we can say \(72\) is a multiple of \(8\) and \(72\) is a multiple of \(9\). We can also say \(72\) is divisible by \(8\) and by \(9\). Another way to talk about this is to say that \(8\) and \(9\) are factors of \(72\). When we write \(72 = 8 ⋅ 9\) we can say that we have factored \(72\).
If \(a • b = m\), then \(a\) and \(b\) are factors of \(m\), and \(m\) is the product of \(a\) and \(b\).
In algebra, it can be useful to determine all of the factors of a number. This is called factoring a number, and it can help us solve many kinds of problems.
For example, suppose a choreographer is planning a dance for a ballet recital. There are 24 dancers, and for a certain scene, the choreographer wants to arrange the dancers in groups of equal sizes on stage.
In how many ways can the dancers be put into groups of equal size? Answering this question is the same as identifying the factors of \(24\). Table \(\PageIndex{6}\) summarizes the different ways that the choreographer can arrange the dancers.
| Number of Groups | Dancers per Group | Total Dancers |
|---|---|---|
| 1 | 24 | 1 • 24 = 24 |
| 2 | 12 | 2 • 12= 24 |
| 3 | 8 | 3 • 8= 24 |
| 4 | 6 | 4 • 6= 24 |
| 6 | 4 | 6 • 4= 24 |
| 8 | 3 | 8 • 3= 24 |
| 12 | 2 | 12 • 2= 24 |
| 24 | 1 | 24 • 1= 24 |
What patterns do you see in Table \(\PageIndex{6}\)? Did you notice that the number of groups times the number of dancers per group is always \(24\)? This makes sense, since there are always \(24\) dancers.
You may notice another pattern if you look carefully at the first two columns. These two columns contain the exact same set of numbers—but in reverse order. They are mirrors of one another, and in fact, both columns list all of the factors of \(24\), which are:
\(1, 2, 3, 4, 6, 8, 12, 24\)
We can find all the factors of any counting number by systematically dividing the number by each counting number, starting with \(1\). If the quotient is also a counting number, then the divisor and the quotient are factors of the number. We can stop when the quotient becomes smaller than the divisor.
Step 1. Divide the number by each of the counting numbers, in order, until the quotient is smaller than the divisor.
- If the quotient is a counting number, the divisor and quotient are a pair of factors.
- If the quotient is not a counting number, the divisor is not a factor.
Step 2. List all the factor pairs.
Step 3. Write all the factors in order from smallest to largest.
Find all the factors of \(72\).
Solution
Divide \(72\) by each of the counting numbers starting with \(1\). If the quotient is a whole number, the divisor and quotient are a pair of factors.
The next line would have a divisor of \(9\) and a quotient of \(8\). The quotient would be smaller than the divisor, so we stop. If we continued, we would end up only listing the same factors again in reverse order. Listing all the factors from smallest to greatest, we have \(1\), \(2\), \(3\), \(4\), \(6\), \(8\), \(9\), \(12\), \(18\), \(24\), \(36\), and \(72\).
Find all the factors of the given number: \(96\)
- Answer
-
\(1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96\)
Find all the factors of the given number: \(80\)
- Answer
-
\(1, 2, 4, 5, 8, 10, 16, 20, 40, 80\)
Contributors and Attributions
- Lynn Marecek (Santa Ana College) and MaryAnne Anthony-Smith (formerly of Santa Ana College). This content produced by OpenStax and is licensed under a Creative Commons Attribution License 4.0 license.


Skip to main content
-
electrophoresis
-
technique used to separate DNA fragments according to size
-
helicase
-
during replication, this enzyme helps to open up the DNA helix by breaking the hydrogen bonds
-
induced mutation
-
mutation that results from exposure to chemicals or environmental agents
-
lagging strand
-
during replication, the strand that is replicated in short fragments and away from the replication fork
-
leading strand
-
strand that is synthesized continuously in the 5'-3' direction, which is synthesized in the direction of the replication fork
-
ligase
-
enzyme that catalyzes the formation of a phosphodiester linkage between the 3' OH and 5' phosphate ends of the DNA
-
mismatch repair
-
type of repair mechanism in which mismatched bases are removed after replication
-
mutation
-
variation in the nucleotide sequence of a genome
-
nucleotide excision repair
-
type of DNA repair mechanism in which the wrong base, along with a few nucleotides upstream or downstream, are removed
-
Okazaki fragment
-
DNA fragment that is synthesized in short stretches on the lagging strand
-
point mutation
-
mutation that affects a single base
-
primase
-
enzyme that synthesizes the RNA primer; the primer is needed for DNA pol to start synthesis of a new DNA strand
-
primer
-
short stretch of nucleotides that is required to initiate replication; in the case of replication, the primer has RNA nucleotides
-
proofreading
-
function of DNA pol in which it reads the newly added base before adding the next one
-
replication fork
-
Y-shaped structure formed during initiation of replication
-
silent mutation
-
mutation that is not expressed
-
single-strand binding protein
-
during replication, protein that binds to the single-stranded DNA; this helps in keeping the two strands of DNA apart so that they may serve as templates
-
sliding clamp
-
ring-shaped protein that holds the DNA pol on the DNA strand
-
spontaneous mutation
-
mutation that takes place in the cells as a result of chemical reactions taking place naturally without exposure to any external agent
-
telomerase
-
enzyme that contains a catalytic part and an inbuilt RNA template; it functions to maintain telomeres at chromosome ends
-
telomere
-
DNA at the end of linear chromosomes
-
topoisomerase
-
enzyme that prevents overwinding of DNA when DNA replication is taking place
-
transformation
-
process in which external DNA is taken up by a cell
-
transition substitution
-
when a purine is replaced with a purine or a pyrimidine is replaced with another pyrimidine
-
transversion substitution
-
when a purine is replaced by a pyrimidine or a pyrimidine is replaced by a purine


8.7: Critical Thinking, Clinical Judgment and the Nursing Profession
Figure 8.12 Image by Moondance from Pixabay
Critical thinking involves the skillful analysis of information to make informed judgments. To engage in critical thinking, it's crucial to recognize and address personal biases and assumptions when encountering information, and to consistently apply standards for evaluating sources.
Critical Thinking in Nursing
Critical thinking is indispensable in nursing as it empowers caregivers to make decisions that optimize patient care. During education, educators and clinical instructors introduced critical-thinking examples in nursing, emphasizing tools for assessment, diagnosis, planning, implementation, and evaluation.
The cultivation of these skills continues into practice. Critical thinking is pivotal in delivering quality patient care and evolves throughout a nursing career, eventually becoming instinctive. Critical thinking in nursing involves identifying problems, determining optimal solutions, and executing effective resolutions through clinical decision-making. Reflection follows action to assess outcomes and consider alternative approaches where necessary.
Nurses play a crucial role as primary patient advocates, often the first to detect changes in status. Critical thinking enables unbiased interpretation of these changes based on evidence rather than conjecture. Anticipating patient needs through critical-thinking skills significantly influences care quality and outcomes.
Key elements of critical thinking in nursing include:
- Clinical judgment: Prioritizing patient needs, interpreting data, and anticipating complications.
- Patient safety: Recognizing deviations and taking preventive actions.
- Communication and collaboration: Fostering interdisciplinary teamwork.
- Problem-solving skills: Analyzing issues and implementing effective solutions.
Developing critical-thinking skills involves continuous learning, reflection on practice, openness to diverse perspectives, and structured problem-solving approaches like SWOT analysis. These skills mature with experience, enabling nurses to navigate complex healthcare scenarios effectively.
In conclusion, critical thinking is indispensable for safe, patient-centered care in nursing. Its ongoing development equips nurses to navigate challenges and uphold standards of excellence in an evolving healthcare landscape.
Clinical Judgement
Clinical judgment is the application of critical thinking to the clinical setting, which includes assessing, analyzing, and synthesizing complex patient data to develop and implement effective patient care plans. It involves interpreting patient information, drawing conclusions, and making decisions about patient care. Clinical judgment centers on interpreting and synthesizing patient data to make informed decisions about nursing interventions. It aims to make accurate and timely clinical decisions that positively impact patient outcomes. Nurses use clinical judgment to prioritize patient needs, anticipate complications, and adapt care plans based on patient responses. It integrates critical thinking skills into real-time clinical situations.
Clinical Decision Making
Clinical decision making refers to the process of choosing the best course of action among various alternatives to achieve a desired patient outcome. It involves selecting appropriate interventions based on a synthesis of clinical judgment, evidence-based practice, patient preferences, and available resources. Clinical decision making is focused on choosing the best action to meet specific patient needs and goals. It aims to provide safe, effective, and patient-centered care. Nurses engage in clinical decision making to determine treatment plans, prioritize care activities, and manage patient responses. It relies on critical thinking and clinical judgment to weigh options and select the most appropriate intervention.
In nursing practice, critical thinking, clinical judgment, and clinical decision-making are interrelated and essential:
- Critical thinking underpins both clinical judgment and decision-making by guiding the analysis and evaluation of information.
- Clinical judgment utilizes critical thinking to interpret patient data and make informed decisions about care priorities and interventions.
- Clinical decision-making integrates critical thinking and clinical judgment to choose effective interventions and strategies for achieving positive patient outcomes.
While critical thinking focuses on the process of reasoning and evaluating information, clinical judgment applies this thinking to clinical situations to interpret and prioritize patient needs. Clinical decision-making then uses critical thinking and clinical judgment to select the best course of action for optimal patient care. Together, these elements form the foundation of professional nursing practice, ensuring safe, effective, and patient-centered care delivery.
Differentiating Between Critical Thinking and Clinical Judgment in Caring for a Patient with Pneumonia
Instructions:
Review the patient scenario provided below. For each action taken by the nurse, determine whether it demonstrates critical thinking or clinical judgment. Write "CT" for critical thinking and "CJ" for clinical judgment next to each action. Explain why you classified each action as either critical thinking or clinical judgment.
Patient Scenario:
Mrs. Johnson, a 68-year-old woman, is admitted to the hospital with pneumonia. She presents with a fever of 101.8°F, productive cough, shortness of breath, and chest pain. Her medical history includes hypertension and type 2 diabetes.
Actions:
1.Reviewing Mrs. Johnson’s Medical History and Lab Results:
- Action: The nurse reviews Mrs. Johnson’s past medical history and her recent lab results to understand her overall health status.
- Classification: ___
- Rationale: ___
2. Administering Prescribed Antibiotics:
- Action: The nurse administers the prescribed antibiotics as ordered by the physician.
- Classification: ___
- Rationale: ___
3. Monitoring Vital Signs:
- Action: The nurse frequently monitors Mrs. Johnson’s vital signs, including temperature, blood pressure, respiratory rate, and oxygen saturation.
- Classification: ___
- Rationale: ___
4. Evaluating the Effectiveness of Interventions:
- Action: After administering antibiotics, the nurse assesses Mrs. Johnson’s response, including a reduction in fever and improvement in breathing.
- Classification: ___
- Rationale: ___
5. Prioritizing Care:
- Action: The nurse prioritizes interventions, ensuring that Mrs. Johnson receives oxygen therapy before other less urgent tasks.
- Classification: ___
- Rationale: ___
6. Educating the Patient and Family:
- Action: The nurse educates Mrs. Johnson and her family about pneumonia, its treatment, and how to manage symptoms at home.
- Classification: ___
- Rationale: ___


1.2.1: Introduction
Learning Objectives
After reading this section, you should be able to answer these questions:
- Why do people become entrepreneurs, and what are the different types of entrepreneurs?
- What characteristics do successful entrepreneurs share?
- How do small businesses contribute to the U.S. economy?
- What are the first steps to take if you are starting your own business?
- Why does managing a small business present special challenges for the owner?
- What are the advantages and disadvantages facing owners of small businesses?
- How does the Small Business Administration help small businesses?
- What trends are shaping entrepreneurship and small-business ownership?
EXPLORING BUSINESS CAREERS
Natalie Tessler, Spa Space
Natalie Tessler has always had an entrepreneurial spirit. After she graduated from New York University’s law school, she began working as a tax attorney for a large firm in Chicago. But Tessler soon realized that this left her feeling unfulfilled. She didn’t want to practice law, and she didn’t want to work for someone else. “I wanted to wake up and be excited for my day,” Tessler said. Not until one night, though, when she was having dinner with a friend who recently had begun a writing career, did she realize it was time. “I was listening to her talk about how much she loved her job. Her passion and excitement—I wanted that. I wanted something that grabbed me and propelled me through the day—and being a lawyer wasn’t it.”
She began searching for what “it” was. She had a tremendous passion and talent for hospitality, entertaining others, and presentation. Seeking an outlet for that flair, she found the spa industry, and the idea for Spa Space was born.
“People think that, owning a spa, I’m able to live this glamorous lifestyle,” she laughs. “Owning a spa is nothing like going to one—my nails always are broken from fixing equipment; my back is usually in pain from sitting hunched over a computer trying to figure out the budget or our next marketing promotion.” Tessler is a true entrepreneur, embodying the spirit and drive necessary to see her vision become a reality.
Tessler wanted to design a spa that focused on something new: creating a comfortable, personalized environment of indulgence while not neglecting the medical technology of proper skincare. “My father’s a dermatologist, so we discussed the importance of making this more than a spa where you can get a frou-frou, smell-good treatment that might actually harm your skin. We both thought it was important to create an experience that is as beneficial for people’s skin as it is for their emotional well-being.” To address this need, Spa Space has a medical advisory board that helps with product selection, treatment design, and staff training.
 Spa Space opened in 2001 and has received a great deal of national recognition for its service excellence, unique treatments and products, and its fresh approach to appealing to both men and women. But it hasn’t always been smooth sailing for Spa Space. Tessler had to steer the business through several obstacles, including the 9/11 tragedy just three months after the spa’s grand opening, and then the Great Recession. Tessler learned to adapt her strategy by refining her target market and the services Spa Space offered. Her resiliency enabled the company to not only survive difficult economic periods, but to thrive and grow 17 years later into what the press recognizes as Chicago’s best spa.
Tessler recently turned the reins over to Ilana Alberico, another entrepreneur and founder of Innovative Spa Management, a company that has been named twice to Inc. magazine’s list of fastest-growing companies. When Alberico met Natalie Tessler and learned about her vision, she was inspired to invest in Spa Space. “Natalie’s vision still resonates... I’m inspired to champion her vision into the future.”
Typical of many who catch the entrepreneurial bug, Natalie Tessler had a vision and pursued it single-mindedly. She is just one of thousands of entrepreneurs from all age groups and backgrounds. Even kids are starting businesses and high-tech firms. College graduates are shunning the corporate world to head out on their own. Downsized employees, mid-career executives, and retirees who have worked for others all their lives are forming the companies they have always wanted to own.
Companies started by entrepreneurs and small-business owners make significant contributions to the U.S. and global economies. Hotbeds of innovation, these small businesses take leadership roles in technological change and the development of new goods and services. Just how important are small businesses to our economy? Table <IP_ADDRESS> provides insight into the role of small business in today’s economy.
You may be one of the millions of Americans who’s considering joining the ranks of business owners. As you read this chapter, you’ll learn why entrepreneurship continues to be one of the hottest areas of business activity. Then you’ll get the information and tools you need to help you decide whether owning your own company is the right career path for you. Next, you’ll discover what characteristics you’ll need to become a successful entrepreneur. Then we’ll look at the importance of small businesses in the economy, guidelines for starting and managing a small business, the many reasons small businesses continue to thrive in the United States, and the role of the Small Business Administration. Finally, the chapter explores the trends that shape entrepreneurship and small-business ownership today.


12.2: Stress in the Health Care System
Stress within any health care profession occurs as a result of the challenging and dynamic conditions experienced in day-to-day work. See Figure 12.1 [1] for an illustration of stress in a health care environment. Nurses and health care professionals are taxed with supporting clients and families in times of extensive life stress and change. Individuals who seek out care often experience rapid life changes as the result of a new diagnosis, altered body function, death of a family member, or significant mental distress. Nurses are frontline staff members who help clients and their families navigate these health stressors. It can be difficult to provide frontline support without taking on some of the stress encountered. As clients and families navigate their feelings of fear, frustration, anxiety, and anger, nurses are often the support members who first hear and react to these feelings. It is important to recognize the constant barrage of these emotions can take a toll, and it is challenging to not assume this emotional burden.
In addition to the emotional burden of providing support for multiple clients and their family members, nurses experience a variety of other stressors inherent to the health care environment itself. These stressors include issues such as environmental stress, increased workload, changing practice conditions, lack of resources, communication barriers, unfavorable working conditions, frequency of engagement with a variety of personnel, challenges in care coordination, workplace violence, alarm fatigue, and staff turnover. Research has identified that the variety of stressors experienced by nursing staff result in inherently greater levels of stress than that experienced in the wider working population. [2] Therefore, nurses must acknowledge the variety of stressors they encounter within the profession and identify strategies to mitigate these forces.
Nursing is charged with emotional situations and topics even on days when no other situational stressors have significant impact. One cannot participate in the significant conversations that accompany health care decision-making, provide patient education, and promote individual coping without acknowledging these conversations are more impactful than deciding, “What should we make for dinner?” By acknowledging this inherent job stress, nurses recognize that eliminating stress within the profession is not possible. There will always be a level of stress that accompanies the health care environment, and this underscores the importance of stress identification, mitigation, and incorporation of stress-reduction strategies. [3]
- “ Emergency_medicine_simulation_training_exercise_in_Balad%2C_Iraq.jpg ” by Robert Couse-Baker is licensed under CC BY 2.0 ↵
- Waddill-Goad, S. (2016). Nurse burnout: Combating stress in nursing. Sigma Theta Tau International. ↵
- Waddill-Goad, S. (2016). Nurse burnout: Combating stress in nursing. Sigma Theta Tau International. ↵


3.6: Modeling temperature and population
- What roles do the parameters \(a\text{,}\) \(k\text{,}\) and \(c\) play in how the function \(F(t) = c + ae^{-kt}\) models the temperature of an object that is cooling or warming in its surroundings?
- How can we use an exponential function to more realistically model a population whose growth levels off?
We've seen that exponential functions can be used to model several different important phenomena, such as the growth of money due to continuously compounded interest, the decay of radioactive quanitities, and the temperature of an object that is cooling or warming due to its surroundings. From initial work with functions of the form \(f(t) = ab^t\) where \(b \gt 0\) and \(b \ne 1\text{,}\) we found that shifted exponential functions of form \(g(t) = ab^t + c\) are also important. Moreover, the special base \(e\) allows us to represent all of these functions through horizontal scaling by writing
where \(k\) is the constant such that \(e^k = b\text{.}\) Functions of the form of Equation (3.6.1) are either always increasing or always decreasing, always have the same concavity, are defined on the set of all real numbers, and have their range as the set of all real numbers greater than \(c\) or all real numbers less than \(c\text{.}\) In whatever setting we are using a model of this form, the crucial task is to identify the values of \(a\text{,}\) \(k\text{,}\) and \(c\text{;}\) that endeavor is the focus of this section.
We have also begun to see the important role that logarithms play in work with exponential models. The natural logarithm is the inverse of the natural exponential function and satisfies the important rule that \(\ln(b^k) = k\ln (b)\text{.}\) This rule enables us to solve equations with the structure \(a^k = b\) for \(k\) in the context where \(a\) and \(b\) are known but \(k\) is not. Indeed, we can first take the natural log of both sides of the equation to get
from which it follows that \(k \ln(a) = \ln(b)\text{,}\) and therefore
Finding \(k\) is often central to determining an exponential model, and logarithms make finding the exact value of \(k\) possible.
In Preview Activity \(\PageIndex{1}\) , we revisit some key algebraic ideas with exponential and logarithmic equations in preparation for using these concepts in models for temperature and population.
In each of the following situations, determine the exact value of the unknown quantity that is identified.
- The temperature of a warming object in an oven is given by \(F(t) = 275 - 203e^{-kt}\text{,}\) and we know that the object's temperature after \(20\) minutes is \(F(20) = 101\text{.}\) Determine the exact value of \(k\text{.}\)
- The temperature of a cooling object in a refrigerator is modeled by \(F(t) = a + 37.4e^{-0.05t}\text{,}\) and the temperature of the refrigerator is \(39.8^\circ\text{.}\) By thinking about the long-term behavior of \(e^{-0.05t}\) and the long-term behavior of the object's temperature, determine the exact value of \(a\text{.}\)
-
Later in this section, we'll learn that one model for how a population grows over time can be given by a function of the form
\[ P(t) = \frac{A}{1 + Me^{-kt}}\text{.} \nonumber \]
Models of this form lead naturally to equations that have structure like
\[ 3 = \frac{10}{1+x}.\label{eq-temp-pop-logistic-structure}\tag{3.6.2} \]Solve Equation (3.6.2) for the exact value of \(x\text{.}\)
- Suppose that \(y = a + be^{-kt}\text{.}\) Solve for \(t\) in terms of \(a\text{,}\) \(b\text{,}\) \(k\text{,}\) and \(y\text{.}\) What does this new equation represent?
Newton's Law of Cooling revisited
In Section 3.2 , we learned that Newton's Law of Cooling, which states that an object's temperature changes at a rate proportional to the difference between its own temperature and the surrounding temperature, results in the object's temperature being modeled by functions of the form \(F(t) = ab^t + c\text{.}\) In light of our subsequent work in Section 3.3 with the natural base \(e\text{,}\) as well as the fact that \(0 \lt b \lt 1\) in this model, we know that Newton's Law of Cooling implies that the object's temperature is modeled by a function of the form
for some constants \(a\text{,}\) \(c\text{,}\) and \(k\text{,}\) where \(k \gt 0\text{.}\)
From Equation (3.6.3), we can determine several different characteristics of how the constants \(a\text{,}\) \(b\text{,}\) and \(k\) are connected to the behavior of \(F\) by thinking about what happens at \(t = 0\text{,}\) at one additional value of \(t\text{,}\) and as \(t\) increases without bound. In particular, note that \(e^{-kt}\) will tend to \(0\) as \(t\) increases without bound.
For the function \(F(t) = ae^{-kt} + c\) that models the temperature of a cooling or warming object, the constants \(a\text{,}\) \(c\text{,}\) and \(k\) play the following roles.
- Since \(e^{-kt}\) tends to \(0\) as \(t\) increases without bound, \(F(t)\) tends to \(c\) as \(t\) increases without bound, and thus \(c\) represents the temperature of the object's surroundings.
- Since \(e^0 = 1\text{,}\) \(F(0) = a + c\text{,}\) and thus the object's initial temperature is \(a + c\text{.}\) Said differently, \(a\) is the difference between the object's initial temperature and the temperature of the surroundings.
- Once we know the values of \(a\) and \(c\text{,}\) the value of \(k\) is determined by knowing the value of the temperature function \(F(t)\) at one nonzero value of \(t\text{.}\)
A can of soda is initially at room temperature, \(72.3^\circ\) Fahrenheit, and at time \(t = 0\) is placed in a refrigerator set at \(37.7^\circ\text{.}\) In addition, we know that after \(30\) minutes, the soda's temperature has dropped to \(59.5^\circ\text{.}\)
- Use algebraic reasoning and your understanding of the physical situation to determine the exact values of \(a\text{,}\) \(c\text{,}\) and \(k\) in the model \(F(t) = ae^{-kt}+c\text{.}\) Write at least one careful sentence to explain your thinking.
- Determine the exact time the object's temperature is \(42.4^\circ\text{.}\) Clearly show your algebraic work and thinking.
- Find the average rate of change of \(F\) on the interval \([25,30]\text{.}\) What is the meaning (with units) of this value?
- If everything stayed the same except the value of \(F(0)\text{,}\) and instead \(F(0) = 65\text{,}\) would the value of \(k\) be larger or smaller? Why?
A more realistic model for population growth
If we assume that a population grows at a rate that is proportionate to the size of the population, it follows that the population grows exponentially according to the model
where \(A\) is the initial population and \(k\) is tied to the rate at which the population grows. Since \(k \gt 0\text{,}\) we know that \(e^{kt}\) is an always increasing, always concave up function that grows without bound. While \(P(t) = Ae^{kt}\) may be a reasonable model for how a population grows when it is relatively small, because the function grows without bound as time increases, it can't be a realistic long-term representation of what happens in reality. Indeed, whether it is the number of fish who can survive in a lake, the number of cells in a petri dish, or the number of human beings on earth, the size of the surroundings and the limitations of resources will keep the population from being able to grow without bound.
In light of these observations, a different model is needed for population, one that grows exponentially at first, but that levels off later. Calculus can be used to develop such a model, and the resulting function is usually called the logistic function , which has form
where \(A\text{,}\) \(M\text{,}\) and \(k\) are positive constants. Since \(k \gt 0\text{,}\) it follows that \(e^{-kt} \to 0\) as \(t\) increases without bound, and thus the denominator of \(P\) approaches \(1\) as time goes on. Thus, we observe that \(P(t)\) tends to \(A\) as \(t\) increases without bound. We sometimes refer to \(A\) as the carrying capacity of the population.
In Desmos , define \(P(t) = \frac{A}{1 + Me^{-kt}}\) and accept sliders for \(A\text{,}\) \(M\text{,}\) and \(k\text{.}\) Set the slider ranges for these parameters as follows: \(0.01 \le A \le 10\text{;}\) \(0.01 \le M \le 10\text{;}\) \(0.01 \le k \le 5\text{.}\)
- Sketch a typical graph of \(P(t)\) on the axes provided and write several sentences to explain the effects of \(A\text{,}\) \(M\text{,}\) and \(k\) on the graph of \(P\text{.}\)
- On a typical logistic graph, where does it appear that the population is growing most rapidly? How is this value connected to the carrying capacity, \(A\text{?}\)
- How does the function \(1 + Me^{-kt}\) behave as \(t\) decreases without bound? What is the algebraic reason that this occurs?
- Use your Desmos worksheet to find a logistic function \(P\) that has the following properties: \(P(0) = 2\text{,}\) \(P(2) = 4\text{,}\) and \(P(t)\) approaches \(9\) as \(t\) increases without bound. What are the approximate values of \(A\text{,}\) \(M\text{,}\) and \(k\) that make the function \(P\) fit these criteria?
Suppose that a population of animals that lives on an island (measured in thousands) is known to grow according to the logistic model, where \(t\) is measured in years. We know the following information: \(P(0) = 2.45\text{,}\) \(P(3) = 4.52\text{,}\) and as \(t\) increases without bound, \(P(t)\) approaches \(11.7\text{.}\)
-
Determine the exact values of \(A\text{,}\) \(M\text{,}\) and \(k\) in the logistic model
\[ P(t) = \frac{A}{1 + Me^{-kt}}\text{.} \nonumber \]
Clearly show your algebraic work and thinking.
- Plot your model from (a) and check that its values match the desired characteristics. Then, compute the average rate of change of \(P\) on the intervals \([0,2]\text{,}\) \([2,4]\text{,}\) \([4,6]\text{,}\) and \([6,8]\text{.}\) What is the meaning (with units) of the values you've found? How is the population growing on these intervals?
- Find the exact time value when the population will be \(10\) (thousand). Show your algebraic work and thinking.
Summary
- When a function of form \(F(t) = c + ae^{-kt}\) models the temperature of an object that is cooling or warming in its surroundings, the temperature of the surroundings is \(c\) because \(e^{-kt} \to 0\) as time goes on, the object's initial temperature is \(a+c\text{,}\) and the constant \(k\) is connected to how rapidly the object's temperature changes. Once \(a\) and \(c\) are known, the constant \(k\) can be determined by knowing the temperature at one additional time, \(t\text{.}\)
-
Because the exponential function \(P(t) = Ae^{kt}\) grows without bound as \(t\) increases, such a function is not a realistic model of a population that we expect to level off as time goes on. The logistic function
\[ P(t) = \frac{A}{1 + Me^{-kt}} \nonumber \]
more appropriately models a population that grows roughly exponentially when \(P\) is small but whose size levels off as it approaches the carrying capacity of the surrounding environment, which is the value of the constant \(A\text{.}\)
Exercises
In Exercise <IP_ADDRESS> below, use the following structure/formula for \(N(t)\text{:}\) \(N(t)=\frac{L}{1+Ab^{-kt}}\text{.}\) In particular, note that when the instructions say “find \(A\)”, this use of “\(A\)” is not in reference to carrying capacity.
A glass filled with ice and water is set on a table in a climate-controlled room with constant temperature of \(71^\circ\) Fahrenheit. A temperature probe is placed in the glass, and we find that the following temperatures are recorded (at time \(t\) in minutes).
| \(t\) | \(0\) | \(20\) |
| \(F(t)\) | \(34.2\) | \(41.7\) |
- Make a rough sketch of how you think the temperature graph should appear. Is the temperature function always increasing? always decreasing? always concave up? always concave down? what's its long-range behavior?
- By desribing \(F\) as a transformation of \(e^t\text{,}\) explain why a function of form \(F(t) = c - ae^{-kt}\text{,}\) where \(a\text{,}\) \(c\text{,}\) and \(k\) are positive constants is an appropriate model for how we expect the temperature function to behave.
- Use the given information to determine the exact values of \(a\text{,}\) \(c\text{,}\) and \(k\) in the model \(F(t) = c - ae^{-kt}\text{.}\)
- Determine the exact time when the water's temperature is \(60^\circ\text{.}\)
A popular cruise ship sets sail in the Gulf of Mexico with \(5000\) passengers and crew on board. Unfortunately, a five family members who board the ship are carrying a highly contagious virus. After interacting with many other passengers in the first few hours of the cruise, all five of them get very sick.
Let \(S(t)\) be the number of people who have acquired the virus \(t\) days after the ship has left port. It turns out that a logistic function is a good model for \(S\text{,}\) and thus we assume that
for some positive constants \(A\text{,}\) \(M\text{,}\) and \(k\text{.}\) Suppose that after \(1\) day, \(20\) people have gotten the virus.
- Recall we know that \(S(0) = 5\) and \(S(1) = 20\text{.}\) In addition, assume that \(5000\) is the number of people who will eventually get sick. Use this information determine the exact values of \(A\text{,}\) \(M\text{,}\) and \(k\) in the logistic model.
- How many days will it take for \(4000\) of the people on the cruise ship to have acquired the virus?
- Compute the average rate of change of \(S\) on the intervals \([1,2]\text{,}\) \([3,4]\text{,}\) and \([5,7]\text{.}\) What is the meaning of each of these values (with units) in the context of the question, and what trend(s) do you observe in these average rates of change?
A closed tank with an inflow and outflow contains a \(100\) liters of saltwater solution. Let the amount of salt in the tank at time \(t\) (in minutes) be given by the function \(A(t)\text{,}\) whose output is measured in grams. At time \(t = 0\) there is an initial amount of salt present in the tank, and the inflow line also carries a saltwater mixture to the tank at a fixed rate; the outflow occurs at the same rate and carries a perfectly mixed solution out of the tank. Because of these conditions, the volume of solution in the tank stays fixed over time, but the amount of salt possibly changes.
It turns out that the problem of determining the amount of salt in the tank at time \(t\) is similar to the problem of determining the temperature of a warming or cooling object, and that the function \(A(t)\) has form
for constants \(a\text{,}\) \(c\text{,}\) and \(k\text{.}\) Suppose that for a particular set of conditions, we know that
Again, \(A(t)\) measures the amount of salt in the tank after \(t\) minutes.
- How much salt is in the tank initially?
- In the long run, how much salt do we expect to eventually be in the tank?
- At what exact time are there exactly \(500\) grams of salt present in the tank?
- Can you determine the concentration of the solution that is being delivered by the inflow to the tank? If yes, explain why and determine this value. If not, explain why that information cannot be found without additional data.


2.16: Introduction to Writing the Right Message
What you’ll learn to do: Write a business communication given a specific audience and purpose
In business, being requested to write a business communication of some type can feel like “one more work assignment.” It is tempting to quickly jot and send that email or letter. However, by doing so, employees may miss the opportunity to help their company do more–and miss the opportunity for advancement. Crafting messages correctly is perhaps the single best way to polish your company’s and your own image.
Focusing the communication effort on the message’s receiver results in business objectives quickly achieved, and growing writer credibility. The results are subtle but the impact is large.
This section begins with two keys to success in business communication: audience and purpose .
The following video introduces a different business communication’s course, but the content is common to all courses.
Contributors and Attributions
- Know Your Audience and Purpose: Professional Writing. Authored by : Saylor.org. Provided by : Saylor.org. Located at : https://www.youtube.com/watch?v=fDz-nq-v3IE . License : CC BY: Attribution
- Introduction to Writing the Right Message. Authored by : Susan Kendall. Provided by : Lumen Learning. License : CC BY: Attribution


6: Definitions and proof methods Last updated Save as PDF Page ID 83425 Jeremy Sylvestre University of Alberta Augustana 6.1: Definitions Definitions are used in mathematics to label objects that have special properties, and to group all such objects together. 6.2: Common mathematical statements In mathematics, we often want to prove that some statement P logically implies some other statement Q; i.e. we want to prove that P⇒Q or (∀x)(P(x)⇒Q(x)). 6.3: Direct Proof The argument A→C1,C1→C2,…,Cm−1→Cm,Cm→B∴A→B is valid (Extended Law of Syllogism). 6.4: Reduction to Cases The following logical equivalence holds: (s1∨s2∨⋯∨sm)→t⇔(s1→t)∧(s2→t)∧⋯∧(sm→t). 6.5: Statements Involving Disjunction First, let's consider a conditional statement with a disjunction on the hypothesis side. 6.6: Proving the contrapositive Modus tollens: P→Q⇔¬Q→¬P. 6.7: Proof by counterexample Sometimes we want to prove that P⇏Q; i.e. that P→Q is not a tautology. 6.8: Proving biconditionals We also often want to prove that two statements P,Q are equivalent; i.e. that P⇔Q. 6.9: Proof by Contradiction


17.3A: Mechanism and Contraction Events of Cardiac Muscle Fibers
Cardiac muscle fibers undergo coordinated contraction via calcium-induced calcium release conducted through the intercalated discs.
- Describe the mechanism and contraction events of cardiac muscle fibers
Key Points
- Cardiac muscle fibers contract via excitation-contraction coupling, using a mechanism unique to cardiac muscle called calcium -induced calcium release.
- Excitation-contraction coupling describes the process of converting an electrical stimulus ( action potential ) into a mechanical response (muscle contraction).
- Calcium-induced calcium release involves the conduction of calcium ions into the cardiomyocyte, triggering further release of ions into the cytoplasm.
- Calcium prolongs the duration of muscle cell depolarization before repolarization occurs.Contraction in cardiac muscle occurs due to the the binding of the myosin head to adenosine triphosphate ( ATP ), which then pulls the actin filaments to the center of the sarcomere, the mechanical force of contraction.
Key Terms
- excitation contraction coupling (ECC) : The physiological process of converting an electrical stimulus to a mechanical response.
- calcium-induced calcium release (CICR) : A process whereby calcium can trigger release of further calcium from the muscle sarcoplasmic reticulum.
Cardiomyocytes are capable of coordinated contraction, controlled through the gap junctions of intercalated discs. The gap junctions spread action potentials to support the synchronized contraction of the myocardium. In cardiac, skeletal, and some smooth muscle tissue, contraction occurs through a phenomenon known as excitation contraction coupling (ECC). ECC describes the process of converting an electrical stimulus from the neurons into a mechanical response that facilitates muscle movement. Action potentials are the electrical stimulus that elicits the mechanical response in ECC.
Calcium-Induced Calcium Release
In cardiac muscle, ECC is dependent on a phenomenon called calcium-induced calcium release (CICR), which involves the influx of calcium ions into the cell, triggering further release of ions into the cytoplasm. The mechanism for CIRC is receptors within the cardiomyocyte that bind to calcium ions when calcium ion channels open during depolarization, releasing more calcium ions into the cell.
Similarly to skeletal muscle, the influx of sodium ions causes an initial depolarization; however, in cardiac muscle, the influx of calcium ions sustains the depolarization so that it lasts longer. CICR creates a “plateau phase” in which the cell’s charge stays slightly positive (depolarized) briefly before it becomes more negative as it repolarizes due to potassium ion influx. Skeletal muscle, by contrast, repolarizes immediately.
Pathway of Cardiac Muscle Contraction
The actual mechanical contraction response in cardiac muscle occurs via the sliding filament model of contraction. In the sliding filament model, myosin filaments slide along actin filaments to shorten or lengthen the muscle fiber for contraction and relaxation. The pathway of contraction can be described in five steps:
- An action potential, induced by the pacemaker cells in the sinoatrial (SA) and atrioventricular (AV) nodes, is conducted to contractile cardiomyocytes through gap junctions.
- As the action potential travels between sarcomeres, it activates the calcium channels in the T-tubules, resulting in an influx of calcium ions into the cardiomyocyte.
- Calcium in the cytoplasm then binds to cardiac troponin-C, which moves the troponin complex away from the actin binding site. This removal of the troponin complex frees the actin to be bound by myosin and initiates contraction.
- The myosin head binds to ATP and pulls the actin filaments toward the center of the sarcomere, contracting the muscle.
- Intracellular calcium is then removed by the sarcoplasmic reticulum, dropping intracellular calcium concentration, returning the troponin complex to its inhibiting position on the active site of actin, and effectively ending contraction as the actin filaments return to their initial position, relaxing the muscle.
Sliding Filament Model of Contraction : Muscle fibers in relaxed (above) and contracted (below) positions
Animation of Myosin and Actin : This animation shows myosin filaments (red) sliding along the actin filaments (pink) to contract a muscle cell.


1.1: Instructions
Why do we fingerspell? Why not just create a sign for everything and not worry about having to spell things out? Like English, the ASL manual alphabet is necessary for spelling proper nouns, names of people, places, and things in addition to short 3-5 letter words that are borrowed from the English language called loan signs. Loan signs make up much of our Restricted Set practice material and you’ll become very familiar with them as the lessons proceed. Before we dive in, a few basics to keep in mind when you are fingerspelling:
- Apostrophes are signed with a twist of the “S” hand
- Double letters are just repeatedly fingerspelled with no special emphasis
- When faced with more than one word, pause slightly between words. For example, when fingerspelling a first and last name you pause in between so the names are distinct and don’t run together.
- Acronyms are signed in small, controlled circles, to alert that this is not a word but letters that form an abbreviation
- Consider breaking longer words into smaller parts, it’s both easier to sign and to understand. Doing so also helps to promote rhythm and flow. This is sometimes referred to as Phonetic Fingerspelling, and we will dive into more details for perfecting this skill in Lesson 8. For example, in RS #1: Jan-u-ary, Feb-ru-ary, Sept-em-ber, Oct-ob-er, Nov-em-ber, Dec-em-ber and so on.
Practice the bulleted fingerspelling basics as you proceed to Restricted Set #1 Calendar Months and Restricted Set #2 Holidays. The reason they are called “restricted” is because they form a subject category, that when kept in mind will provide a context for what may come off a partner’s hand. If you know the Restricted Set is Months, you can be assured that twelve words will be fingerspelled and begin to anticipate the letters that may be coming. You could also utilize the process of elimination. Fingerspelling is a very active process and Restricted Sets enable us to engage our mindfulness to practice our anticipation skills and build confidence for success.


7.7: Language Development in the School-Age Child
selected template will load here
This action is not available.
Human language is the most complex behavior on the planet and, at least as far as we know, in the universe. Language involves both the ability to comprehend (receptive) spoken and written (expressive) words and to create communication in real-time when we speak or write. Most languages are oral, generated through speaking. Speaking involves a variety of complex cognitive, social, and biological processes including operation of the vocal cords, and the coordination of breath with movements of the throat and mouth, and tongue. Other languages are sign languages, in which the communication is expressed by movements of the hands. The most common sign language is American Sign Language (ASL), currently spoken by more than 500,000 people in the United States alone.
Although language is often used for the transmission of information (“turn right at the next light and then go straight,” “Place tab A into slot B”), this is only its most mundane function. Language also allows us to access existing knowledge, to draw conclusions, to set and accomplish goals, and to understand and communicate complex social relationships. Language is fundamental to our ability to think, and without it, we would be nowhere near as intelligent as we are.
Language can be conceptualized in terms of sounds, meaning, and the environmental factors that help us understand it. Phonemes are the elementary sounds of our language, morphemes are the smallest units of meaning in a language, syntax is the set of grammatical rules that control how words are put together, and contextual information is the elements of communication that are not part of the content of language but that help us understand its meaning. Understanding how language works means reaching across many branches of psychology—everything from basic neurological functioning to high-level cognitive processing. Language shapes our social interactions and brings order to our lives. Complex language is one of the defining factors that make us human.49
49. Beginning Psychology – Intelligence and Language by Charles Stangor is licensed under CC BY-NC-SA 3.0


4.3: 1898
-
- Last updated
- Save as PDF
Although the United States had a long history of international economic, military, and cultural engagement that stretched back deep into the eighteenth century, the Spanish-American and Philippine-American Wars (1898–1902) marked a crucial turning point in American interventions abroad. In pursuing war with Spain, and then engaging in counterrevolutionary conflict in the Philippines, the United States expanded the scope and strength of its global reach. Over the next two decades, the United States would become increasingly involved in international politics, particularly in Latin America. These new conflicts and ensuing territorial problems forced Americans to confront the ideological elements of imperialism. Should the United States act as an empire? Or were foreign interventions and the taking of territory antithetical to its founding democratic ideals? What exactly would be the relationship between the United States and its territories? And could colonial subjects be successfully and safely incorporated into the body politic as American citizens? The Spanish-American and Philippine-American Wars brought these questions, which had always lurked behind discussions of American expansion, out into the open.
In 1898, Americans began in earnest to turn their attention southward to problems plaguing their neighbor Cuba. Since the middle of the nineteenth century, Cubans had tried unsuccessfully again and again to gain independence from Spain. The latest uprising, and the one that would prove fatal to Spain’s colonial designs, began in 1895 and was still raging in the winter of 1898. By that time, in an attempt to crush the uprising, Spanish general Valeriano Weyler y Nicolau had been conducting a policy of reconcentration—forcing Cubans living in certain cities to relocate en masse to military camps—for about two years. Prominent newspaper publishers sensationalized Spanish atrocities. Cubans in the United States and their allies raised cries of Cuba Libre! And while the U.S. government proclaimed a wish to avoid armed conflict with Spain, President McKinley became increasingly concerned about the safety of American lives and property in Cuba. He ordered the battleship Maine to Havana harbor in January 1898.
The Maine sat undisturbed in the harbor for about two weeks. Then, on the evening of February 15, a titanic explosion tore open the ship and sent it to the bottom of the ocean. Three quarters of the ship’s 354 occupants died. A naval board of inquiry immediately began an investigation to ascertain the cause of the explosion, but the loudest Americans had already decided that Spanish treachery was to blame. Capitalizing on the outrage, “yellow journals”—newspapers that promoted sensational stories, notoriously at the cost of accuracy—such as William Randolph Hearst’s New York Journal called for war with Spain. When urgent negotiations failed to produce a mutually agreeable settlement, Congress officially declared war on April 25.
Although America’s war effort began haphazardly, Spain’s decaying military crumbled. Military victories for the United States came quickly. In the Pacific, on May 1, Commodore George Dewey engaged the Spanish fleet outside Manila, the capital of the Philippines (another Spanish colonial possession), destroyed it, and proceeded to blockade Manila harbor. Two months later, American troops took Cuba’s San Juan Heights in what would become the most well-known battle of the war, winning fame not for regular soldiers but for the irregular, especially Theodore Roosevelt and his Rough Riders. Roosevelt had been the assistant secretary of the navy but had resigned his position in order to see action in the war. His actions in Cuba made him a national celebrity. As disease began to eat away at American troops, the Spanish suffered the loss of Santiago de Cuba on July 17, effectively ending the war. The two nations agreed to a cease-fire on August 12 and formally signed the Treaty of Paris in December. The terms of the treaty stipulated, among other things, that the United States would acquire Spain’s former holdings of Guam, Puerto Rico, and the Philippines.
Secretary of state John Hay memorably referred to the conflict as a “splendid little war,” and at the time it certainly appeared that way. Fewer than four hundred Americans died in battle in a war that lasted about fifteen weeks. Contemporaries celebrated American victories as the providential act of God. The influential Brooklyn minister Lyman Abbott, for instance, declared that Americans were “an elect people of God” and saw divine providence in Dewey’s victory at Manila. 9 Some, such as Senator Albert J. Beveridge of Indiana, took matters one step further, seeing in American victory an opportunity for imperialism. In Beveridge’s view, America had a “mission to perform” and a “duty to discharge” around the world. 10 What Beveridge envisioned was nothing less than an American empire.
But the question of whether the United States should become an empire was sharply debated across the nation in the aftermath of the Spanish-American War and the acquisition of Hawaii in July 1898. At the behest of American businessmen who had overthrown the Hawaiian monarchy, the United States annexed the Hawaiian Islands and their rich plantations. Between Hawaii and a number of former Spanish possessions, many Americans coveted the economic and political advantages that increased territory would bring. Those opposed to expansion, however, worried that imperial ambitions did not accord with the nation’s founding ideals. American actions in the Philippines brought all of these discussions to a head.
The Philippines were an afterthought of the Spanish-American War, but when the smoke cleared, the United States found itself in possession of a key foothold in the Pacific. After Dewey’s victory over the Spanish fleet in the Battle of Manila Bay, conversations about how to proceed occupied the attentions of President McKinley, political leaders from both parties, and the popular press. American and Philippine forces (under the leadership of Emilio Aguinaldo) were in communication: Would the Americans offer their support to the Filipinos and their ongoing efforts against the Spanish? Or would the Americans replace the Spanish as a colonial occupying force? American forces were instructed to secure Manila without allowing Philippine forces to enter the Walled City (the seat of the Spanish colonial government), hinting, perhaps, at things to come. Americans wondered what would happen next. Perhaps a good many ordinary Americans shared the bewildered sentiments of Mr. Dooley, the fictional Irish-American barkeeper whom humorist Finley Peter Dunne used to satirize American life: “I don’t know what to do with th’ Ph’lippeens anny more thin I did las’ summer, befure I heerd tell iv thim. . . . We can’t sell thim, we can’t ate thim, an’ we can’t throw thim into the th’ alley whin no wan is lookin’’.” 11
As debates about American imperialism continued against the backdrop of an upcoming presidential election, tensions in the Philippines escalated. Emilio Aguinaldo was inaugurated as president of the First Philippine Republic (or Malolos Republic) in late January 1899; fighting between American and Philippine forces began in early February; and in April 1899, Congress ratified the 1898 Treaty of Paris, which concluded the Spanish-American War and gave Spain $20 million in exchange for the Philippine Islands. 12
Like the Cubans, Filipinos had waged a long war against their Spanish colonizers. The United States could have given them the independence they had long fought for, but, instead, at the behest of President William McKinley, the United States occupied the islands and from 1899 to 1902 waged a bloody series of conflicts against Filipino insurrectionists that cost far more lives than the war with Spain. Under the leadership of Emilio Aguinaldo, Filipinos who had fought for freedom against the Spanish now fought for freedom against the very nation that had claimed to have liberated them from Spanish tyranny. 13
The Philippine Insurrection, or the Philippine-American War, was a brutal conflict of occupation and insurgency. Contemporaries compared the guerrilla-style warfare in challenging and unfamiliar terrain to the American experiences in the Indian Wars of the late nineteenth century. Many commented on its brutality and the uncertain mission of American troops. An April 1899 dispatch from a Harper’s Weekly correspondent began, “A week has passed—a week of fighting and marching, of jungles and rivers, of incident and adventure so varied and of so rapid transition that to sit down to write about it makes one feel as if he were trying to describe a dream where time, space, and all the logical sequences of ordinary life are upset in the unrelenting brutality of war.” 14 John Bass described his experiences in detail, and his reportage, combined with accounts that came directly from soldiers, helped shape public knowledge about the war. Reports of cruelty on both sides and a few high-profile military investigations ensured continued public attention to events across the Pacific.
Amid fighting to secure the Philippine Islands, the federal government sent two Philippine Commissions to assess the situation in the islands and make recommendations for a civilian colonial government. A civilian administration, with William H. Taft as the first governor-general (1901–1903), was established with military support. Although President Theodore Roosevelt declared the war to be over in 1902, resistance and occasional fighting continued into the second decade of the twentieth century. 15
Debates about American imperialism dominated headlines and tapped into core ideas about American identity and the proper role of the United States in the larger world. Should a former colony, established on the principles of freedom, liberty, and sovereignty, become a colonizer itself? What was imperialism, anyway? Many framed the Filipino conflict as a Protestant, civilizing mission. Others framed American imperialism in the Philippines as nothing new, as simply the extension of a never-ending westward American expansion. It was simply destiny. Some saw imperialism as a way to reenergize the nation by asserting national authority and power around the globe. Others baldly recognized the opportunities the Philippine Islands presented for access to Asian markets. But critics grew loud. The American Anti-Imperialist League, founded in 1899 and populated by such prominent Americans as Mark Twain, Andrew Carnegie, and Jane Addams, protested American imperial actions and articulated a platform that decried foreign subjugation and upheld the rights of all to self-governance. Still others embraced anti-imperialist stances because of concerns about immigration and American racial identity, afraid that American purity stood imperiled by contact with strange and foreign peoples. For whatever reason, however, the onset or acceleration of imperialism was a controversial and landmark moment in American history. America had become a preeminent force in the world.


29.10B: Varicose Veins
Varicose veins, typically found in the legs, are those that have become enlarged and tortuous due to malfunctioning valves.
- Describe the cause of varicose veins
Key Points
- Veins have leaflet valves to prevent blood from flowing backwards; this backflow is called retrograde or reflux flow. The muscles of the leg pump the veins to return blood to the heart against the effects of gravity.
- When veins become varicose, the leaflets of the valves no longer meet properly, and the valves no longer work, a situation called valvular incompetence. This causes pooling of blood and enlargement of the veins.
- Varicose veins are more common in women than in men, and are linked with heredity. Other related factors are pregnancy, obesity, menopause, aging, prolonged standing, leg injury, abdominal straining, and crossing legs at the knees or ankles.
- Non-surgical treatments for varicose veins include elastic stockings, elevating the legs, and exercise. The traditional surgical treatment has been vein stripping, or removal of the affected veins.
Key Terms
- superficial veins : Those veins that are close to the surface of the body.
- tortuous : Twisted; having many turns; convoluted.
Varicose veins are those that have become enlarged and tortuous, commonly affecting the legs.
Causes of Varicose Veins
Varicose Veins : This image shows a normal vein with a working valve and normal blood flow. Figure B shows a varicose vein with a deformed valve, abnormal blood flow, and thin, stretched walls. The middle image shows where varicose veins might appear in a leg.
Veins have leaflet valves to prevent blood from flowing backwards; this backflow is called retrograde or reflux flow. The muscles of the leg pump the veins to return blood to the heart against the effects of gravity. When veins become varicose, the leaflets of the valves no longer meet properly, and the valves no longer work. This change is called valvular incompetence, and it allows blood to flow backwards. To accommodate the retrograde or reflux flow, the veins enlarge even more.
Leg with Varicose Veins : A man with many varicose veins in the lower leg.
Varicose veins are most often found in the superficial veins of the legs, which are subject to high pressure when standing. In addition to cosmetic concerns, varicose veins are often painful, especially when standing or walking. They can often itch, and scratching them can lead to skin ulcers.
Varicose veins are more common in women than in men, and are linked with heredity. Other related factors are pregnancy, obesity, menopause, aging, prolonged standing, leg injury, abdominal straining, and crossing legs at the knees or ankles. They are distinguished from “spider veins,” which are also due to valvular incompetence, by their size. Spider veins are less than one millimeter in diameter, whereas varicose veins are larger than this in diameter.
Treatments
Non-surgical treatments for varicose veins include elastic stockings, elevating the legs, and exercise. The traditional surgical treatment has been vein stripping, or removal of the affected veins. Because most of the blood in the legs is returned by the deep veins, the superficial veins, which return only about 10 per cent of the total blood of the legs, can usually be removed without serious harm.


The Middle East is perceived as predominantly “Islamic” due to the Muslim majority of the region’s population, but large numbers of non-Muslims reside there, and pre-Islamic influences remain significant. While it’s thought of as an Islamic region, the Eastern Orthodox Christian Church is a significant part of the region, for example. Its origins are rooted in Greek-speaking communities of the Eastern Mediterranean. Their split from Rome, what is now known as the Great Schism, was likely as related to the linguistic and cultural divide as much as to theological differences between the bishops of the Eastern Mediterranean and of the Western Mediterranean (Matejic, 2012).
This chapter therefore provides an overview of the predominant religions of the Middle East, including Islam, Judaism, Christianity, and Zoroastrianism, but there is significant diversity beyond these four religions. There are a number religious minorities, which may be sub-sets of a major religion, a case of religious syncretism, or something completely outside of those traditions.
THE ABRAHAMIC FAITHS
The monotheistic religions of Judaism, Christianity and Islam, are sometimes referred to as “Abrahamic Faiths” because of their shared heritage stemming from the patriarch, Abraham. Within these faiths there are many sub-categories, in addition to religious traditions of the region that came before Abraham, such as Zoroastrianism. Its founder, Zoroaster, was born in what is now Afghanistan, and the faith continues among a small number of adherents in Iran, India, and other parts of the world. Muslim and non-Muslim communities in Iran, Afghanistan, Pakistan, and Central Asian countries continue to practice its traditions alongside their religious practices. For example, marking the Spring Equinox in the festival of Now Ruz is a major traditional holiday in Iran, Afghanistan, Central Asia, and Pakistan.
There are general cultural aspects shared by Judaism, Christianity and Islam. They each:
• Were founded by a Semitic person or people;
• Refer to the same God: Yahweh in Hebrew; Jehovah in English; Allah in Arabic; Khuda in Persian.
• Use similar concepts of Justice. For example the idea that one should always consider God to be present when one is judging. Other than murder, adultery and stealing, bearing false witness was one of the most egregious crimes in the societies in which these religions originated.
Islam and Judaism have more doctrinal similarities with each other than they have with Christianity, especially in regard to their concepts of monotheism (God being without offspring or partner – this is a specific reference to Surat al-Ikhlas of the Qur’an in Islam – ), their legal systems and in their rigorous restrictions on daily life and practice, such as their protocols for diet. However, unlike Judaism, both Islam and Christianity are universal religions; i.e., one needn’t be born into it to participate in the religion. The following religious comparison grid provides key areas of similarity and difference amongst them.
Abrahamic Religions Comparison Chart
Belief/ Practice
Judaism
Christianity
Islam
Concept of God, monotheism
One god, considered as creator and sustainer of the universe. Worship of any additional gods is discouraged by banning images of humans and animals which could potentially be idols.
One god, considered as creator and sustainer of the universe. God as cause of Mary’s immaculate conception, and “father” of Jesus.
One god, considered as creator and sustainer of the universe. God possesses no partner, no offspring. Worship of any additional gods, or idols, is strictly forbidden. Worship of any additional gods is discouraged by banning images of humans and animals which could potentially be idols.
Messengers of God/ Prophets
Belief in prophets of God.
Belief in prophets of God. Jesus is considered the Son of God.
Belief in prophets of God. Belief that Muhammad is the last of God’s prophets. Jesus is considered a prophet.
Timing for weekly worship/ community gathering.
This is a day of rest, Friday evening through Saturday evening is a time of required rest from normal daily work. Synagogue services on Saturday are a time designated for community.
This is a day of rest, Community worship on Sunday. It is a required day of rest from normal daily work.
Friday is the day for group prayer. Work is allowed, however.
Scripture
Torah (including the Ten Commandments).
Torah (including the Ten Commandments); New Testament.
Torah (including the Ten Commandments); Psalms; Gospels of the Christian Bible; Qur’an
Adam and Eve as the first humans; the great flood;
Adam and Eve as the first humans; the great flood;
Adam and Eve as the first humans; the great flood;
Alms
Tithing, or giving a portion of your wealth to those in need.
Tithing, or giving a portion of your wealth to those in need.
Alms, or Zaka, is one of the five pillars
Circumcision
Required for males.
Not required.
Required for males.
Pilgrimage
Was required, until the temple in Jerusalem was destroyed.
not required. many pilgrimage sites, however.
required to Mekka. tombs and shrines that may also pilgrimage sites.
Ritual Use of Water
Ablutions before prayer, and traditionally before entering the Temple in Jerusalem.
Holy water is used before entering a church, to bless worshipers during mass, and to baptize.
Ablutions are required before prayer.
Messianic expectations
The king will one day return.
Jesus will return on Judgment day
Shi’is expect the rightly-guided Imam, or Mahdi, to return.
Supernatural entities
Angels
Angels, Satan/ Lucifer
Angels, Jinn, Satan, or Shaytan/Iblis
Fasting and Dietary restrictions
Fasting for Yom Kippur. Multiple restrictions and requirements for preparation, including the way to slaughter animals. No pork. Ritual use of alcohol.
Fasting for lent. Eastern Orthodox Christianity requires a vegetarian diet for lent. Pork is allowed. Ritual use of alcohol.
Fasting for Ramadan. Multiple restrictions and requirements for preparation, including the way to slaughter animals.