7.18: Laws Affecting Human Resource Practices
- List the protected employee classes in the United States.
- Summarize the key laws related to employee discrimination.
- Explain what HR managers can do to protect the company against discrimination lawsuits.
- Explain HR’s role in workplace safety.
- Explain collective bargaining and the law that governs it.
Protected Classes of Employees
Certain groups of employees are legally protected from discrimination. In other words, if an employee belongs to a protected group and is discriminated against because of his or her status as a member of that group, that employee can take legal action against the employer. But being part of a protected group does not mean an employee can never be disciplined or fired.
For example, imagine a female employee who shows up late, meets few of her goals, and receives a poor evaluation. She applies for promotion but loses out to a white man who has worked hard, met his goals, and received a very positive evaluation. In this case, the woman was not discriminated against because of her gender; rather, she was denied promotion because of poor work performance. As a result, she would not have legal cause for action.
On the other hand, imagine a Latino employee who has a stellar work record. He is laid off, whereas a Caucasian worker with a poor work record is kept on. In this case, there is a good chance the Latino employee could win a legal case against his employer for racial discrimination.
HR managers can protect the company against discrimination lawsuits by understanding discrimination law and putting policies into place to avoid discrimination. Should discrimination occur despite workplace policies against it, HR managers can work with upper management to quickly address individual issues, compensate employees, and discipline managers who discriminate. The Equal Employment Opportunity Commission (EEOC) is responsible for interpreting and enforcing the laws against discrimination in the workplace.
Employers may not discriminate against employees because of:
- Race or Color: This category includes blacks, whites, people of Latino or Asian origin or descent, and indigenous peoples.
- National Origin: This means employers may not discriminate based on the country where a person was born or the country from which his or her ancestors came—unless language or other requirements make it impossible for the individual to do the job effectively. For example, a native Russian speaker with no English language skills could reasonably be denied a job as a lecturer in a U.S. college.
- Sex: This means an employer cannot discriminate against either men or women as a result of their gender. Title VII as it is currently interpreted provides protection based on gender identity or sexual orientation. To quote the EEOC “these protections apply regardless of any contrary state or local laws.” [1]
- Religion: According to the EEOC, protections “include moral or ethical beliefs as to what is right and wrong which are sincerely held with the strength of traditional religious views.” Employers must “reasonably accommodate to an employee’s or prospective employee’s religious observance or practice” unless doing so would impose an “undue hardship on the conduct of the employer’s business.”
Key Laws Related to Employee Discrimination
Employee discrimination has been the focus of several important laws. They include the following:
Equal Pay Act of 1963: This law makes it illegal to pay men more than women for the same work.
Civil Rights Act of 1964 : This act is intended to protect people who were often discriminated against because of their race, national origin, gender, color, or religion. The Title VII of the act relates specifically to employment. The law, which applies to any company with more than fifteen employees, also makes it illegal to discriminate against an employee because she is pregnant or coping with conditions (such as morning sickness) caused by pregnancy. New rules also provide some protections to transgender individuals. Title VII also created the EEOC to implement the law.
Age Discrimination in Employment Act of 1967: This law, which applies to companies with twenty-plus employees, makes it illegal to discriminate against employees because they are more than forty years old.
Pregnancy Discrimination Act of 1978: This act amended Title VII of the Civil Rights Act to also prohibit discrimination on the basis of pregnancy.
Americans with Disabilities Act of 1990: According to this act, employers must make “reasonable” workplace modifications to accommodate the needs of a person with a disability. Examples include addition of ramps for wheelchairs, adjustments to work schedules, etc.
Family Medical Leave Act of 1993: This law offers job protections to individuals for parental leave and medical leave. For covered employers, a parent may take up to 12 weeks after the birth of a child.
Uniformed Services Employment and Reemployment Rights Act of 1994 (USERRA): This law offers job protections to individuals when they are called to uniformed service.
Genetic Information Nondiscrimination Act of 2008: According to this act, genetic information cannot be used to make employment or health insurance decisions.
In addition to these laws, there are also several that relate only to federal government employees. These include sections 501 and 505 of the Rehabilitation Act of 1973 and the Civil Service Reform Act of 1978. Individual states also have their own employee protection laws; for example, some states forbid discrimination based on sexual orientation, weight, marital status, etc.
Workplace Safety
There are a number of laws in place in the United States that require employers to provide a safe workplace. These laws are administered by OSHA, but HR must be sure the laws are followed. In some occupations, however, safety can’t be guaranteed. For example, when employees work with hazardous chemicals, large machinery, transportation vehicles, etc., there are risks. Workers have the right to refuse to work in dangerous conditions without risking their jobs.
To lower risk, management and HR can work together to substitute less dangerous procedures or materials when both options can get the job done, isolate dangerous materials or machines from employees who do not need to work with them, ensure that proper safety equipment and ventilation are used in all hazardous situations, put policies in place that decrease risk by taking required safety precautions, and require employees to use appropriate safety equipment such as goggles, gloves, and hard hats. All these positive changes can help the company by keeping employees on the job, thus increasing productivity. Research shows that safety programs more than pay for themselves. [2]
Collective Bargaining
A 2004 story in the New York Times describes how, until recently, workers were locked into a building while working at night for Sam’s Club:
Looking back to that night, Michael Rodriguez still has trouble believing the situation he faced when he was stocking shelves on the overnight shift at the Sam’s Club in Corpus Christi, Tex.
It was 3 a.m., Mr. Rodriguez recalled, some heavy machinery had just smashed into his ankle, and he had no idea how he would get to the hospital.
The Sam’s Club, a Wal-Mart subsidiary, had locked its overnight workers in, as it always did, to keep robbers out and, as some managers say, to prevent employee theft. As usual, there was no manager with a key to let Mr. Rodriguez out. The fire exit, he said, was hardly an option – management had drummed into the overnight workers that if they ever used that exit for anything but a fire, they would lose their jobs. [3]
How could employees respond to such a terrible situation? Individual employees have few choices: they can stay and cope with the situation, they can complain and face the possibility of being fired, or they can quit. Labor unions—groups of employees acting together—can give employees more leverage. Although one worker had little power to make change, large groups in unions could threaten strikes or slowdowns to force change.
Today, labor unions and employers make agreements through a process called collective bargaining. Collective bargaining is the process by which employers work with union representatives to decide on policies, wages, and benefits. Union representatives are empowered to speak on behalf of the entire union. If the union representative negotiates a raise for its members, all members get more money.
Labor unions gained much of their power through the Wagner Act of 1935. The act made it legal for most workers to organize or join labor unions. It also made it possible for labor unions to negotiate contracts for their members. To help labor unions become more effective, the act set up the National Labor Relations Board (NLRB).
The NLRB oversees the rules and policies related to collective bargaining. According to the NLRB: “If a union is selected as the representative of employees, the employer and union are required to meet at reasonable times to bargain in good faith about wages, hours, and other mandatory subjects. Even after a contract expires, the parties must bargain in good faith for a successor contract, or the termination of the agreement, while terms of the expired contract continue.” The NLRB also provides many specific rules for negotiation, mediation, and arbitration in the case of a disagreement between employer and labor.
- https://www.eeoc.gov/eeoc/newsroom/wysk/enforcement_protections_lgbt_workers.cfm ↵
- David Machles, “Evaluating the Effectiveness of Safety Training,” June 01, 2003, accessed July 26, 2017, https://ohsonline.com/Articles/2003/06/Evaluating-the-Effectiveness-of-Safety-Training.aspx . ↵
- Steven Greenhouse, “Workers Assail Night Lock-Ins By Wal-Mart,” Jan. 18, 2004, accessed July 26, 2017, http://www.nytimes.com/2004/01/18/us/workers-assail-night-lock-ins-by-wal-mart.html?mcubz=2 . ↵
Contributors and Attributions
- Laws Affecting Human Resource Practices. Authored by : Lisa Jo Rudy and Lumen Learning. License : CC BY: Attribution
- Image: Gavel. Authored by : Activedia. Located at : https://pixabay.com/en/law-justice-court-judge-legal-1063249/ . License : CC BY: Attribution
- Worker in hard hat. Authored by : Shawn T Moore. Provided by : U.S. Department of Labor. Located at : https://www.flickr.com/photos/usdol/26772672461/ . License : Public Domain: No Known Copyright


2.15: CTE - Multimedia Studies
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- Susan Rahman, Prateek Sunder, and Dahmitra Jackson
- CC ECHO
Multimedia expression involves storytelling at its most advanced, whether it be for Hollywood big screens, apps on our smartphones or shiny and bright online advertising, a multimedia studies certificate affords a student entry into the world of cultural creation.According to the College of Marin Career Technical Education website,
Multimedia Entertainment Designers use design skills,equipment and technology to produce audio/video content, visual effects, 2D and 3D animations for use in video production, video games, presentations, marketing materials and educational training. They create moving visuals that excite, explain and entertain.Multimedia Entertainment Designers may work in the entertainment industry in video production, modeling or visual effect creation for movie, television, and game development. Or, they may work for schools,corporations or organizations to create eye-catching motion graphics and animations for use in presentations,marketing materials and educational training.(Multimedia–Entertainment, n.d.)
The variety and scope of what a certificate in Multimedia studies can lead to is clearly vast and highly relevant in our ever more digitally accessed world. Often, the type of imagery and storytelling afforded those who create media can and do fall prey to the tropes and stereotypes that so often perpetuate racist, sexist and heteronormative narratives. A 2015 study by Kassia E. Kulaszewicz at the School of Social Work at St. Catherine University and the University of St.Thomas St. Paul, Minnesota discusses just this and how the media influences perceptions on racism and racial biases. Historically, people of color (POC) were largely unable to portray themselves in the media. POC representations were not first-hand accounts of their own stories, beliefs, opinions, culture, or identities, rather an imagined creation by those who controlled the industry. The media was, and in most parts, still is, controlled by white elites at the head of media corporations, who have been able to solely dictate how people of color were portrayed in films, the news, literature, and other forms of media. The research done by Kulaszewicz also incorporates Bandura’s Learning Theory to understand how media messages can influence beliefs and values in the same way Bandura (and many others) postulates that social behaviors can be learned through others. (Kulaszewicz, 2015).
It is important to know what information is available to media consumers, and how the information consumed shapes, influences, and impacts individual agency, as well as thoughts,beliefs, and behaviors towards people of color. Kulaszewicz specifically focuses on the perceptions, stereotypes, racial micro aggressions, and perceived racial differences of African American males and finds that the skewed or limited information provided by media about a group a viewer otherwise does not have contact with leaves them only with what is provided in the media they consume which is often partial and filled with racial stereotypes (Kulaszewicz,2015).
Language or word choice is also of significance in terms of how stereotypes and racists beliefs are constructed in the media. The use of identifier word patterns, using the words “black” and“white” to depict things either seen as positive or negative help shape racialized beliefs.Onaverage, the word “black” is used three times more than the word “white” in the news. The constant usage of the word “black” in a negative connotation can extend into a micro aggression, as it conditions and socializes the mind to correlate the word to negative thoughts and ideas (Kulaszewicz, 2015). Black men are often criminalized in the media, and the research revealed patterns of criminalization and justification for this criminalization in the stories we are told. In contrast, in the case of police brutality, when a White officer shoots or commits other excessive and unnecessary acts of violence against a Black man, the officer and their actions are supported regardless of their own criminality. The research suggests that a correlation exists between the media and racism; specifically, media that reinforces racism and perpetuates racial stereotypes, thus exacerbating systemic inequality and racism (Kulaszewicz,2015). As multimedia students and scholars undertake re-imaging imagery and storytelling, they have an obligation to commit to changing the narrative so often found in mainstream media. Only then can we move past the damaging ways in which our systems of media have solidified the structures of racial and gendered inequality.


7.2: Modeling the evolution of discrete states
So far, we have only dealt with continuously varying characters. However, many characters of interest to biologists are best defined as characters with a set number of fixed states. For limblessness in squamates, each species is either legless (state 0) or not (state 1; actually, there are some species that might be considered “intermediate” Brandley et al. 2008, but we will ignore those for now) . We might have particular questions about the evolution of limblessness in squamates. For example, how many times this character has changed in the evolutionary history of squamates? How often does limblessness evolve? Do limbs ever re-evolve? Is the evolution of limblessness related to some other aspect of the lives of these reptiles?
We will consider discrete characters where each species might exhibit one of k states. (In the limbless example above, k = 2). For characters with more than two states, there is a key distinction between ordered and unordered characters. Ordered characters can be placed in an order so that transitions only occur between adjacent states. For example, I might include “intermediate” species that are somewhere in between limbed and limbless – for example, the “mermaid skinks” ( Sirenoscincus ) from Madagascar, so called because they lack hind limbs (Figure 7.2, Moch and Senter 2011) . An ordered model might only allow transitions between limbless and intermediate, and intermediate and limbed; it would be impossible under such a model to go directly from limbed to limbless without first becoming intermediate. For unordered characters, any state can change into any other state. In this chapter, I will focus mainly on unordered characters; we will return to ordered characters later in the book.
Most work on the evolution of discrete characters on phylogenetic trees has focused on the evolution of gene or protein sequences. Gene sequences are made up of four character states (A, C, T, and G for DNA). Models of sequence evolution allow transitions among all of these states at certain rates, and may allow transition rates to vary across sites, among clades, or through time. There are a huge number of named models that have been applied to this problem (e.g. Jukes-Cantor, JC; General Time-Reversible, GTR; and many more, Yang 2006) , and a battery of statistical approaches are available to fit these models to data (e.g. Posada 2008) .
Any discrete character can be modeled in a similar way as gene sequences. When considering phenotypic characters, we should keep in mind two main differences from the analysis of DNA sequences. First, arbitrary discrete characters may have any number of states (beyond the four associated with DNA sequence data). Second, characters are typically analyzed independently rather than combining long sets of characters and assuming that they share the same model of change.


8.2: Fitting Exponential Models to Data
In this section, you will:
- Build an exponential model from data.
- Build a logarithmic model from data.
- Build a logistic model from data.
In previous sections of this chapter, we were either given a function explicitly to graph or evaluate, or we were given a set of points that were guaranteed to lie on the curve. Then we used algebra to find the equation that fit the points exactly. In this section, we use a modeling technique called regression analysis to find a curve that models data collected from real-world observations. With regression analysis , we don’t expect all the points to lie perfectly on the curve. The idea is to find a model that best fits the data. Then we use the model to make predictions about future events.
Do not be confused by the word model . In mathematics, we often use the terms function , equation , and model interchangeably, even though they each have their own formal definition. The term model is typically used to indicate that the equation or function approximates a real-world situation.
We will concentrate on three types of regression models in this section: exponential, logarithmic, and logistic. Having already worked with each of these functions gives us an advantage. Knowing their formal definitions, the behavior of their graphs, and some of their real-world applications gives us the opportunity to deepen our understanding. As each regression model is presented, key features and definitions of its associated function are included for review. Take a moment to rethink each of these functions, reflect on the work we’ve done so far, and then explore the ways regression is used to model real-world phenomena.
 What do these phenomena have in common? For one thing, all the models either increase or decrease as time moves forward. But that’s not the whole story. It’s the way data increase or decrease that helps us determine whether it is best modeled by an exponential equation. Knowing the behavior of exponential functions in general allows us to recognize when to use exponential regression, so let’s review exponential growth and decay.
Recall that exponential functions have the form or When performing regression analysis, we use the form most commonly used on graphing utilities, Take a moment to reflect on the characteristics we’ve already learned about the exponential function (assume
- must be greater than zero and not equal to one.
-
The initial value of the model is
- If the function models exponential growth. As increases, the outputs of the model increase slowly at first, but then increase more and more rapidly, without bound.
- If the function models exponential decay . As increases, the outputs for the model decrease rapidly at first and then level off to become asymptotic to the x -axis. In other words, the outputs never become equal to or less than zero.
As part of the results, your calculator will display a number known as the correlation coefficient , labeled by the variable or (You may have to change the calculator’s settings for these to be shown.) The values are an indication of the “goodness of fit” of the regression equation to the data. We more commonly use the value of instead of but the closer either value is to 1, the better the regression equation approximates the data.
Exponential Regression
Exponential regression is used to model situations in which growth begins slowly and then accelerates rapidly without bound, or where decay begins rapidly and then slows down to get closer and closer to zero. We use the command “ ExpReg ” on a graphing utility to fit an exponential function to a set of data points. This returns an equation of the form,
Note that:
- must be non-negative.
- when we have an exponential growth model.
- when we have an exponential decay model.
How To
Given a set of data, perform exponential regression using a graphing utility.
-
Use the
STAT
then
EDIT
menu to enter given data.
- Clear any existing data from the lists.
- List the input values in the L1 column.
- List the output values in the L2 column.
-
Graph and observe a scatter plot of the data using the
STATPLOT
feature.
- Use ZOOM [ 9 ] to adjust axes to fit the data.
- Verify the data follow an exponential pattern.
-
Find the equation that models the data.
- Select “ ExpReg ” from the STAT then CALC menu.
- Use the values returned for a and b to record the model,
- Graph the model in the same window as the scatterplot to verify it is a good fit for the data.
Example 1
Using Exponential Regression to Fit a Model to Data
In 2007, a university study was published investigating the crash risk of alcohol impaired driving. Data from 2,871 crashes were used to measure the association of a person’s blood alcohol level (BAC) with the risk of being in an accident. Table 1 shows results from the study 9 . The relative risk is a measure of how many times more likely a person is to crash. So, for example, a person with a BAC of 0.09 is 3.54 times as likely to crash as a person who has not been drinking alcohol.
| BAC | 0 | 0.01 | 0.03 | 0.05 | 0.07 | 0.09 |
| Relative Risk of Crashing | 1 | 1.03 | 1.06 | 1.38 | 2.09 | 3.54 |
| BAC | 0.11 | 0.13 | 0.15 | 0.17 | 0.19 | 0.21 |
| Relative Risk of Crashing | 6.41 | 12.6 | 22.1 | 39.05 | 65.32 | 99.78 |
- Answer
-
-
Using the
STAT
then
EDIT
menu on a graphing utility, list the
BAC
values in L1 and the relative risk values in L2. Then use the
STATPLOT
feature to verify that the scatterplot follows the exponential pattern shown in
Figure 1
:
Use the “ ExpReg ” command from the STAT then CALC menu to obtain the exponential model,
Converting from scientific notation, we have:
Notice that which indicates the model is a good fit to the data. To see this, graph the model in the same window as the scatterplot to verify it is a good fit as shown in Figure 2 :
-
Use the model to estimate the risk associated with a BAC of
Substitute
for
in the model and solve for
If a 160-pound person drives after having 6 drinks, he or she is about 26.35 times more likely to crash than if driving while sober.
-
Using the
STAT
then
EDIT
menu on a graphing utility, list the
BAC
values in L1 and the relative risk values in L2. Then use the
STATPLOT
feature to verify that the scatterplot follows the exponential pattern shown in
Figure 1
:
Try It #1
Table 2 shows a recent graduate’s credit card balance each month after graduation.
| Month | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| Debt ($) | 620.00 | 761.88 | 899.80 | 1039.93 | 1270.63 | 1589.04 | 1851.31 | 2154.92 |
Q&A
Is it reasonable to assume that an exponential regression model will represent a situation indefinitely?
No. Remember that models are formed by real-world data gathered for regression. It is usually reasonable to make estimates within the interval of original observation (interpolation). However, when a model is used to make predictions, it is important to use reasoning skills to determine whether the model makes sense for inputs far beyond the original observation interval (extrapolation).
Building a Logarithmic Model from Data
Just as with exponential functions, there are many real-world applications for logarithmic functions: intensity of sound, pH levels of solutions, yields of chemical reactions, production of goods, and growth of infants. As with exponential models, data modeled by logarithmic functions are either always increasing or always decreasing as time moves forward. Again, it is the way they increase or decrease that helps us determine whether a logarithmic model is best.
Recall that logarithmic functions increase or decrease rapidly at first, but then steadily slow as time moves on. By reflecting on the characteristics we’ve already learned about this function, we can better analyze real world situations that reflect this type of growth or decay. When performing logarithmic regression analysis , we use the form of the logarithmic function most commonly used on graphing utilities, For this function
- All input values, must be greater than zero.
- The point is on the graph of the model.
- If the model is increasing. Growth increases rapidly at first and then steadily slows over time.
- If the model is decreasing. Decay occurs rapidly at first and then steadily slows over time.
Logarithmic Regression
Logarithmic regression is used to model situations where growth or decay accelerates rapidly at first and then slows over time. We use the command “LnReg” on a graphing utility to fit a logarithmic function to a set of data points. This returns an equation of the form,
Note that
- all input values, must be non-negative.
- when the model is increasing.
- when the model is decreasing.
How To
Given a set of data, perform logarithmic regression using a graphing utility.
-
Use the
STAT
then
EDIT
menu to enter given data.
- Clear any existing data from the lists.
- List the input values in the L1 column.
- List the output values in the L2 column.
-
Graph and observe a scatter plot of the data using the
STATPLOT
feature.
- Use ZOOM [ 9 ] to adjust axes to fit the data.
- Verify the data follow a logarithmic pattern.
-
Find the equation that models the data.
- Select “ LnReg ” from the STAT then CALC menu.
- Use the values returned for a and b to record the model,
- Graph the model in the same window as the scatterplot to verify it is a good fit for the data.
Example 2
Using Logarithmic Regression to Fit a Model to Data
Due to advances in medicine and higher standards of living, life expectancy has been increasing in most developed countries since the beginning of the 20th century.
Table 3 shows the average life expectancies, in years, of Americans from 1900–2010 10 .
| Year | 1900 | 1910 | 1920 | 1930 | 1940 | 1950 |
| Life Expectancy(Years) | 47.3 | 50.0 | 54.1 | 59.7 | 62.9 | 68.2 |
| Year | 1960 | 1970 | 1980 | 1990 | 2000 | 2010 |
| Life Expectancy(Years) | 69.7 | 70.8 | 73.7 | 75.4 | 76.8 | 78.7 |
- Answer
-
-
ⓐ
Using the
STAT
then
EDIT
menu on a graphing utility, list the years using values 1–12 in L1 and the corresponding life expectancy in L2. Then use the
STATPLOT
feature to verify that the scatterplot follows a logarithmic pattern as shown in
Figure 3
:
Use the “ LnReg ” command from the STAT then CALC menu to obtain the logarithmic model,
Next, graph the model in the same window as the scatterplot to verify it is a good fit as shown in Figure 4 :
-
ⓐ
Using the
STAT
then
EDIT
menu on a graphing utility, list the years using values 1–12 in L1 and the corresponding life expectancy in L2. Then use the
STATPLOT
feature to verify that the scatterplot follows a logarithmic pattern as shown in
Figure 3
:
Try It #2
Sales of a video game released in the year 2000 took off at first, but then steadily slowed as time moved on. Table 4 shows the number of games sold, in thousands, from the years 2000–2010.
| Year | 2000 | 2001 | 2002 | 2003 | 2004 | 2005 |
| Number Sold (thousands) | 142 | 149 | 154 | 155 | 159 | 161 |
| Year | 2006 | 2007 | 2008 | 2009 | 2010 | - |
| Number Sold (thousands) | 163 | 164 | 164 | 166 | 167 | - |
Building a Logistic Model from Data
Like exponential and logarithmic growth, logistic growth increases over time. One of the most notable differences with logistic growth models is that, at a certain point, growth steadily slows and the function approaches an upper bound, or limiting value . Because of this, logistic regression is best for modeling phenomena where there are limits in expansion, such as availability of living space or nutrients.
It is worth pointing out that logistic functions actually model resource-limited exponential growth. There are many examples of this type of growth in real-world situations, including population growth and spread of disease, rumors, and even stains in fabric. When performing logistic regression analysis , we use the form most commonly used on graphing utilities:
Recall that:
- is the initial value of the model.
- when the model increases rapidly at first until it reaches its point of maximum growth rate, At that point, growth steadily slows and the function becomes asymptotic to the upper bound
- is the limiting value, sometimes called the carrying capacity , of the model.
Logistic Regression
Logistic regression is used to model situations where growth accelerates rapidly at first and then steadily slows to an upper limit. We use the command “Logistic” on a graphing utility to fit a logistic function to a set of data points. This returns an equation of the form
Note that
- The initial value of the model is
- Output values for the model grow closer and closer to as time increases.
How To
Given a set of data, perform logistic regression using a graphing utility.
-
Use the
STAT
then
EDIT
menu to enter given data.
- Clear any existing data from the lists.
- List the input values in the L1 column.
- List the output values in the L2 column.
-
Graph and observe a scatter plot of the data using the
STATPLOT
feature.
- Use ZOOM [ 9 ] to adjust axes to fit the data.
- Verify the data follow a logistic pattern.
-
Find the equation that models the data.
- Select “ Logistic ” from the STAT then CALC menu.
- Use the values returned for and to record the model,
- Graph the model in the same window as the scatterplot to verify it is a good fit for the data.
Example 3
Using Logistic Regression to Fit a Model to Data
Mobile telephone service has increased rapidly in America since the mid 1990s. Today, almost all residents have cellular service. Table 5 shows the percentage of Americans with cellular service between the years 1995 and 2012 11 .
| Year | Americans with Cellular Service (%) | Year | Americans with Cellular Service (%) |
|---|---|---|---|
| 1995 | 12.69 | 2004 | 62.852 |
| 1996 | 16.35 | 2005 | 68.63 |
| 1997 | 20.29 | 2006 | 76.64 |
| 1998 | 25.08 | 2007 | 82.47 |
| 1999 | 30.81 | 2008 | 85.68 |
| 2000 | 38.75 | 2009 | 89.14 |
| 2001 | 45.00 | 2010 | 91.86 |
| 2002 | 49.16 | 2011 | 95.28 |
| 2003 | 55.15 | 2012 | 98.17 |
- Answer
-
-
ⓐ
Using the
STAT
then
EDIT
menu on a graphing utility, list the years using values 0–15 in L1 and the corresponding percentage in L2. Then use the
STATPLOT
feature to verify that the scatterplot follows a logistic pattern as shown in
Figure 5
:
Use the “ Logistic ” command from the STAT then CALC menu to obtain the logistic model,
Next, graph the model in the same window as shown in Figure 6 the scatterplot to verify it is a good fit:
-
To approximate the percentage of Americans with cellular service in the year 2013, substitute
for the in the model and solve for
According to the model, about 99.3% of Americans had cellular service in 2013.
- The model gives a limiting value of about 105. This means that the maximum possible percentage of Americans with cellular service would be 105%, which is impossible. (How could over 100% of a population have cellular service?) If the model were exact, the limiting value would be and the model’s outputs would get very close to, but never actually reach 100%. After all, there will always be someone out there without cellular service!
-
ⓐ
Using the
STAT
then
EDIT
menu on a graphing utility, list the years using values 0–15 in L1 and the corresponding percentage in L2. Then use the
STATPLOT
feature to verify that the scatterplot follows a logistic pattern as shown in
Figure 5
:
Try It #3
Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to 2012.
| Year | Seal Population (Thousands) | Year | Seal Population (Thousands) |
|---|---|---|---|
| 1997 | 3.493 | 2005 | 19.590 |
| 1998 | 5.282 | 2006 | 21.955 |
| 1999 | 6.357 | 2007 | 22.862 |
| 2000 | 9.201 | 2008 | 23.869 |
| 2001 | 11.224 | 2009 | 24.243 |
| 2002 | 12.964 | 2010 | 24.344 |
| 2003 | 16.226 | 2011 | 24.919 |
| 2004 | 18.137 | 2012 | 25.108 |
Media
Access this online resource for additional instruction and practice with exponential function models.
Choosing an Appropriate Model for Data
Now that we have discussed various mathematical models, we need to learn how to choose the appropriate model for the raw data we have. Many factors influence the choice of a mathematical model, among which are experience, scientific laws, and patterns in the data itself. Not all data can be described by elementary functions. Sometimes, a function is chosen that approximates the data over a given interval. For instance, suppose data were gathered on the number of homes bought in the United States from the years 1960 to 2013. After plotting these data in a scatter plot, we notice that the shape of the data from the years 2000 to 2013 follow a logarithmic curve. We could restrict the interval from 2000 to 2010, apply regression analysis using a logarithmic model, and use it to predict the number of home buyers for the year 2015.
Three kinds of functions that are often useful in mathematical models are linear functions, exponential functions, and logarithmic functions. If the data lies on a straight line, or seems to lie approximately along a straight line, a linear model may be best. If the data is non-linear, we often consider an exponential or logarithmic model, though other models, such as quadratic models, may also be considered.
In choosing between an exponential model and a logarithmic model, we look at the way the data curves. This is called the concavity. If we draw a line between two data points, and all (or most) of the data between those two points lies above that line, we say the curve is concave down. We can think of it as a bowl that bends downward and therefore cannot hold water. If all (or most) of the data between those two points lies below the line, we say the curve is concave up. In this case, we can think of a bowl that bends upward and can therefore hold water. An exponential curve, whether rising or falling, whether representing growth or decay, is always concave up away from its horizontal asymptote. A logarithmic curve is always concave away from its vertical asymptote. In the case of positive data, which is the most common case, an exponential curve is always concave up, and a logarithmic curve always concave down.
A logistic curve changes concavity. It starts out concave up and then changes to concave down beyond a certain point, called a point of inflection.
After using the graph to help us choose a type of function to use as a model, we substitute points, and solve to find the parameters. We reduce round-off error by choosing points as far apart as possible.
Does a linear, exponential, logarithmic, or logistic model best fit the values listed in Table \( \PageIndex{ 1 } \)? Find the model, and use a graph to check your choice.
| \(x\) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| \(y\) | 0 | 1.386 | 2.197 | 2.773 | 3.219 | 3.584 | 3.892 | 4.159 | 4.394 |
- Solution
-
First, plot the data on a graph as in Figure \( \PageIndex{ 8 } \). For the purpose of graphing, round the data to two decimal places.
Figure \( \PageIndex{ 8 } \)Clearly, the points do not lie on a straight line, so we reject a linear model. If we draw a line between any two of the points, most or all of the points between those two points lie above the line, so the graph is concave down, suggesting a logarithmic model. We can try \(y=aln(bx)\). Plugging in the first point, \(( \text{1,0} )\text{,}\) gives \(0=alnb\). We reject the case that \(a=0\) (if it were, all outputs would be 0), so we know \(ln(b)=0\). Thus \(b=1\) and \(y=aln( \text{x} )\). Next we can use the point \(( \text{9,4}\text{.394} )\) to solve for \(a\):\[y=aln(x) 4.394=aln(9) a= 4.394 ln(9) \nonumber \]
Because \(a= 4.394 ln( 9 ) \approx 2\), an appropriate model for the data is \(y=2ln( x )\).
To check the accuracy of the model, we graph the function together with the given points as in Figure \( \PageIndex{ 9 } \).
Figure \( \PageIndex{ 9 } \) The graph of \(y=2lnx\).We can conclude that the model is a good fit to the data.
Compare Figure \( \PageIndex{ 9 } \) to the graph of \(y=ln( x 2 )\) shown in Figure \( \PageIndex{ 10 } \).
Figure \( \PageIndex{ 10 } \) The graph of \(y=ln( x 2 )\)The graphs appear to be identical when \(x>0\). A quick check confirms this conclusion: \(y=ln( x 2 )=2ln( x )\) for \(x>0\).
However, if \(x<0\), the graph of \(y=ln( x 2 )\) includes a "extra" branch, as shown in Figure \( \PageIndex{ 11 } \). This occurs because, while \(y=2ln( x )\) cannot have negative values in the domain (as such values would force the argument to be negative), the function \(y=ln( x 2 )\) can have negative domain values.
Figure \( \PageIndex{ 11 } \)
Does a linear, exponential, or logarithmic model best fit the data in Table \( \PageIndex{ 2 } \)? Find the model.
| \(x\) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| \(y\) | 3.297 | 5.437 | 8.963 | 14.778 | 24.365 | 40.172 | 66.231 | 109.196 | 180.034 |


5.1: Why It Matters- Plate Tectonics
Recognize the ongoing development of, evidence for, and large scale planetary effects of the Theory of Plate Tectonics.
Introduction
Plate tectonics is often seen as the missing piece of the puzzle for geologists. Plate tectonics explains, either directly or indirectly, just about every topic discussed in geology. It is the glue that binds everything together. Before plate tectonics, geologists had no explanation for these (and other) questions:
- What causes the tectonic plates to move the way they do?
- Why is the oceanic crust younger than continental crust?
- Why do the continents look the way they do, like puzzle pieces or are positioned as they are?
- Why are Japan and California so prone to earthquakes and volcanoes?
- How did the Himalayas form?
- Why do we find evidence of aquatic species at the very top of the Himalayas and other mountainous areas?
- How do mountains form?
- Why do the oceans look the way they do?
- What factors contributed to the occurrence of the ice ages?
- Why the same species can be found on continents on opposite sides of the oceans?
As you move through this section, keep in mind all of these questions and make note of any other impacts the Theory of Plate Tectonics has had on the field of geology.
Learning Outcomes
- Describe Continental Drift including supporting evidence.
- Critique and interpret major types of evidence supporting the Theory of Plate Tectonics.
- Describe different geological processes in relation to plate tectonics.
Contributors and Attributions
CC licensed content, Original
- Authored by : Kimberly Schulte and Lumen Learning. Provided by : Lumen Learning. License : CC BY: Attribution


7.1: Cauchy's Theorem
Introduction
Our main goal is a better understanding of the partial fraction expansion of a given transfer function. With respect to the example that closed the discussion of complex differentiation, see the equation - In this equation, we found
\[(zI-B)^{-1} = \frac{1}{z-\lambda_{1}}P_{1}+\frac{1}{(z-\lambda_{1})^2}D_{1}+\frac{1}{z-\lambda_{2}}P_{2} \nonumber\]
where the \(P_{j}\) and \(D_{j}\) enjoy the amazing properties
\[ \begin{align*} BP_{1} &= P_{1}B \\[4pt] &= \lambda_{1}P_{1}+D_{1} \end{align*}\]
and
\[BP_{2} = P_{2}B = \lambda_{2}P_{2} \nonumber\]
\[P_{1}+P_{2} = I \nonumber\]
\[P_{1}^{2} = P_{1} \nonumber\]
\[P_{2}^{2} = P_{2} \nonumber\]
and
\[D_{1}^{2} = 0 \nonumber\]
\[P_{1}D_{1} = D_{1}P_{1} \nonumber\]
\[= D_{1} \nonumber\]
and
\[P_{2}D_{1} = D_{1}P_{2} = 0\]
In order to show that this always happens, i.e., that it is not a quirk produced by the particular \(B\), we require a few additional tools from the theory of complex variables. In particular, we need the fact that partial fraction expansions may be carried out through complex integration.
Integration of Complex Functions Over Complex Curves
We shall be integrating complex functions over complex curves. Such a curve is parameterized by one complex valued or, equivalently, two real valued, function(s) of a real parameter (typically denoted by \(t\)). More precisely,
\[C \equiv \{z(t) = x(t)+iy(t) | a \le t \le b\} \nonumber\]
For example, if \(x(t) = y(t) = t\) while \(a = 0\) and \(b = 1\), then \(C\) is the line segment joining \(0+i0\) to \(1+i\).
We now define
\[\int f(z) dz = \equiv \int_{a}^{b} f(z(t)) z'(t) dt \nonumber\]
For example, if \(C = \{t+it | 0 \le t \le 1\}\) as above and \(f(z) = z\) then
\[\int z dz = \int_{0}^{1} (t+it) (1+i) dt = \int_{0}^{1} t-t+i2t dt = i \nonumber\]
while if \(C\) is the unit circle \(\{e^{it} | 0 \le t \le 2\pi\}\) then
\[\int z dz =\in_{0}^{2\pi} e^{it}ie^{it} dt = i \int_{0}^{2\pi} e^{i2t} dt = i \int_{0}^{2\pi} \cos(2t)+i \sin(2t) dt = 0 \nonumber\]
Remaining with the unit circle but now integrating \(f(z) = \frac{1}{z}\) we find
\[\int z^{-1} dz = \int_{0}^{2 \pi} e^{-(it)}ie^{it} dt = 2\pi i \nonumber\]
We generalize this calculation to arbitrary (integer) powers over arbitrary circles. More precisely, for integer mm and fixed complex \( (z-a)^{m}\) over
\[C(a,r) \equiv \{a+re^{it} | 0 \le t \le 2\pi\} \nonumber\]
the circle of radius \(r\) centered at \(a\)
\[\int (z-a)^{m} dz = \int_{0}^{2\pi} (a+re^{it}-a)^{m} rie^{it} dt \nonumber\]
\[= ir^{m+1} \int_{0}^{2\pi} e^{i(m+1)t} dt \nonumber\]
\[\int (z-a)^{m} dz = ir^{m+1} \int_{0}^{2\pi} \cos((m+1)t)+i \sin((m+1)t) dt = \left \{ \begin{array}{cc} {2\pi i}&{\text{if} m = -1}\\ {0}&{\text{otherwise}} \end{array} \right . \nonumber\]
When integrating more general functions it is often convenient to express the integral in terms of its real and imaginary parts. More precisely
\[\begin{align*} \int f(z) dz &=\int u(x,y)+iv(x,y) dx+i \int u(x,y)+iv(x,y) dy \\[4pt] &=\int u(x,y)dx - \int v(x,y) dy+i \int v(x,y)dx+i \int u(x,y) dy \\[4pt] &=\int_{a}^{b} u(x(t), y(t))x'(t)-v(x(t), y(t))y'(t) dt+i \int_{a}^{b} u(x(t), y(t))y'(t)+v(x(t), y(t))x'(t) dt \end{align*}\]
The second line should invoke memories of:
If \(C\) is a closed curve and \(M\) and \(N\) are continuously differentiable real-valued functions on \(C_{in}\), the region enclosed by \(C\), then
\[\int M dx+ \int N dy = \iint \frac{\partial N}{\partial x}-\frac{\partial M}{\partial y} dxdy \nonumber\]
Applying this to the situation above, we find, so long as \(C\) is closed, that
\[\int f(z) dz = -\iint \frac{\partial v}{\partial x}+\frac{\partial u}{\partial y} dxdy+ i \iint \frac{\partial u}{\partial x}+\frac{\partial v}{\partial y} dxdy \nonumber\]
At first glance it appears that Green's Theorem only serves to muddy the waters. Recalling the Cauchy-Riemann equations however we find that each of these double integrals is in fact identically zero! In brief, we have proven:
If \(f\) is differentiable on and in the closed curve \(C\) then \(\int f(z) dz = 0\).
Strictly speaking, in order to invoke Green's Theorem we require not only that ff be differentiable but that its derivative in fact be continuous. This however is simply a limitation of our simple mode of proof; Cauchy's Theorem is true as stated.
This theorem, together with \(C(a,r) \equiv \{a+re^{it} | 0 \le t \le 2\pi\}\), permits us to integrate every proper rational function. More precisely, if \(q = \frac{f}{g}\) where \(f\) is a polynomial of degree at most \(m-1\) and \(g\) is an mth degree polynomial with h distinct zeros at \(\{\lambda_{j} | j = \{1, \cdots, h\}\}\) with respective multiplicities of \(\{m_{j} | j = \{1, \cdots, h\}\}\) we found that
\[q(z) = \sum_{j = 1}^{h} \sum_{k = 1}^{m_{j}} \frac{q_{j,k}}{(z-\lambda_{j})^{k}} \nonumber\]
Observe now that if we choose \(r_{j}\) so small that \(\lambda_{j}\) is the only zero of \(g\) encircled by \(C_{j} \equiv C(\lambda_{j}, r_{j})\) then by Cauchy's Theorem
\[\int q(z) dz = \sum_{k = 1}^{m_{j}} q_{j,k} \int \frac{1}{(z-\lambda_{j})^k} dz \nonumber\]
In Equation we found that each, save the first, of the integrals under the sum is in fact zero. Hence,
\[\int q(z) dz = 2\pi i q_{j,1} \nonumber\]
With \(q_{j,1}\) in hand, say from this equation or
residue
, one may view Equation as a means for computing the indicated integral. The opposite reading, i.e., that the integral is a convenient means of expressing \(q_{j,1}\), will prove just as useful. With that in mind, we note that the remaining residues may be computed as integrals of the product of q and the appropriate factor. More precisely,
\[ \int q(z)(z-\lambda_{j})^{k-1} dz = 2\pi i q_{j,k} \nonumber\]
One may be led to believe that the precision of this result is due to the very special choice of curve and function. We shall see ...


10.7: Mutations and Genetic Diseases
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- Deboleena Roy (American River College)
- American River College
Learning Objectives
- To describe the causes of genetic mutations and how they lead to genetic diseases.
We have seen that the sequence of nucleotides in a cell’s deoxyribonucleic acid (DNA) is what ultimately determines the sequence of amino acids in proteins made by the cell and thus is critical for the proper functioning of the cell. On rare occasions, however, the nucleotide sequence in DNA may be modified either spontaneously (by errors during replication, occurring approximately once for every 10 billion nucleotides) or from exposure to heat, radiation, or certain chemicals. Any chemical or physical change that alters the nucleotide sequence in DNA is called a mutation. When a mutation occurs in an egg or sperm cell that then produces a living organism, it will be inherited by all the offspring of that organism.
Common types of mutations include substitution (a different nucleotide is substituted), insertion (the addition of a new nucleotide), and deletion (the loss of a nucleotide). These changes within DNA are called point mutations because only one nucleotide is substituted, added, or deleted (Figure \(\PageIndex{1}\)). Because an insertion or deletion results in a frame-shift that changes the reading of subsequent codons and, therefore, alters the entire amino acid sequence that follows the mutation, insertions and deletions are usually more harmful than a substitution in which only a single amino acid is altered.
The chemical or physical agents that cause mutations are called mutagens. Examples of physical mutagens are ultraviolet (UV) and gamma radiation. Radiation exerts its mutagenic effect either directly or by creating free radicals that in turn have mutagenic effects. Radiation and free radicals can lead to the formation of bonds between nitrogenous bases in DNA. For example, exposure to UV light can result in the formation of a covalent bond between two adjacent thymines on a DNA strand, producing a thymine dimer (Figure \(\PageIndex{2}\)). If not repaired, the dimer prevents the formation of the double helix at the point where it occurs. The genetic disease xeroderma pigmentosum is caused by a lack of the enzyme that cuts out the thymine dimers in damaged DNA. Individuals affected by this condition are abnormally sensitive to light and are more prone to skin cancer than normal individuals.
Sometimes gene mutations are beneficial, but most of them are detrimental. For example, if a point mutation occurs at a crucial position in a DNA sequence, the affected protein will lack biological activity, perhaps resulting in the death of a cell. In such cases the altered DNA sequence is lost and will not be copied into daughter cells. Nonlethal mutations in an egg or sperm cell may lead to metabolic abnormalities or hereditary diseases. Such diseases are called inborn errors of metabolism or genetic diseases. A partial listing of genetic diseases is presented in Figure \(\PageIndex{1}\), and two specific diseases are discussed in the following sections. In most cases, the defective gene results in a failure to synthesize a particular enzyme.
| Disease | Responsible Protein or Enzyme |
|---|---|
| alkaptonuria | homogentisic acid oxidase |
| galactosemia | galactose 1-phosphate uridyl transferase, galactokinase, or UDP galactose epimerase |
| Gaucher disease | glucocerebrosidase |
| gout and Lesch-Nyhan syndrome | hypoxanthine-guanine phosphoribosyl transferase |
| hemophilia | antihemophilic factor (factor VIII) or Christmas factor (factor IX) |
| homocystinuria | cystathionine synthetase |
| maple syrup urine disease | branched chain α-keto acid dehydrogenase complex |
| McArdle syndrome | muscle phosphorylase |
| Niemann-Pick disease | sphingomyelinase |
| phenylketonuria (PKU) | phenylalanine hydroxylase |
| sickle cell anemia | hemoglobin |
| Tay-Sachs disease | hexosaminidase A |
| tyrosinemia | fumarylacetoacetate hydrolase or tyrosine aminotransferase |
| von Gierke disease | glucose 6-phosphatase |
| Wilson disease | Wilson disease protein |
PKU results from the absence of the enzyme phenylalanine hydroxylase. Without this enzyme, a person cannot convert phenylalanine to tyrosine, which is the precursor of the neurotransmitters dopamine and norepinephrine as well as the skin pigment melanin.
When this reaction cannot occur, phenylalanine accumulates and is then converted to higher than normal quantities of phenylpyruvate. The disease acquired its name from the high levels of phenylpyruvate (a phenyl ketone) in urine.
PKU may be diagnosed by assaying a sample of blood or urine for phenylalanine or one of its metabolites. Medical authorities recommend testing every newborn’s blood for phenylalanine within 24 h to 3 weeks after birth. If the condition is detected, mental retardation can be prevented by immediately placing the infant on a diet containing little or no phenylalanine. Because phenylalanine is plentiful in naturally produced proteins, the low-phenylalanine diet depends on a synthetic protein substitute plus very small measured amounts of naturally produced foods. Before dietary treatment was introduced in the early 1960s, severe mental retardation was a common outcome for children with PKU. Prior to the 1960s, 85% of patients with PKU had an intelligence quotient (IQ) less than 40, and 37% had IQ scores below 10. Since the introduction of dietary treatments, however, over 95% of children with PKU have developed normal or near-normal intelligence. The incidence of PKU in newborns is about 1 in 12,000 in North America.
Every state in the United States has mandated that screening for PKU be provided to all newborns.
Several genetic diseases are collectively categorized as lipid-storage diseases . Lipids are constantly being synthesized and broken down in the body, so if the enzymes that catalyze lipid degradation are missing, the lipids tend to accumulate and cause a variety of medical problems. When a genetic mutation occurs in the gene for the enzyme hexosaminidase A, for example, gangliosides cannot be degraded but accumulate in brain tissue, causing the ganglion cells of the brain to become greatly enlarged and nonfunctional. This genetic disease, known as Tay-Sachs disease , leads to a regression in development, dementia, paralysis, and blindness, with death usually occurring before the age of three. There is currently no treatment, but Tay-Sachs disease can be diagnosed in a fetus by assaying the amniotic fluid (amniocentesis) for hexosaminidase A. A blood test can identify Tay-Sachs carriers—people who inherit a defective gene from only one rather than both parents—because they produce only half the normal amount of hexosaminidase A, although they do not exhibit symptoms of the disease.
Looking Closer: Recombinant DNA Technology
More than 3,000 human diseases have been shown to have a genetic component, caused or in some way modulated by the person’s genetic composition. Moreover, in the last decade or so, researchers have succeeded in identifying many of the genes and even mutations that are responsible for specific genetic diseases. Now scientists have found ways of identifying and isolating genes that have specific biological functions and placing those genes in another organism, such as a bacterium, which can be easily grown in culture. With these techniques, known as recombinant DNA technology , the ability to cure many serious genetic diseases appears to be within our grasp.
Isolating the specific gene or genes that cause a particular genetic disease is a monumental task. One reason for the difficulty is the enormous amount of a cell’s DNA, only a minute portion of which contains the gene sequence. Thus, the first task is to obtain smaller pieces of DNA that can be more easily handled. Fortunately, researchers are able to use restriction enzymes (also known as restriction endonucleases), discovered in 1970, which are enzymes that cut DNA at specific, known nucleotide sequences, yielding DNA fragments of shorter length. For example, the restriction enzyme EcoRI recognizes the nucleotide sequence shown here and cuts both DNA strands as indicated:
Once a DNA strand has been fragmented, it must be cloned; that is, multiple identical copies of each DNA fragment are produced to make sure there are sufficient amounts of each to detect and manipulate in the laboratory. Cloning is accomplished by inserting the individual DNA fragments into phages (bacterial viruses) that can enter bacterial cells and be replicated. When a bacterial cell infected by the modified phage is placed in an appropriate culture medium, it forms a colony of cells, all containing copies of the original DNA fragment. This technique is used to produce many bacterial colonies, each containing a different DNA fragment. The result is a DNA library , a collection of bacterial colonies that together contain the entire genome of a particular organism.
The next task is to screen the DNA library to determine which bacterial colony (or colonies) has incorporated the DNA fragment containing the desired gene. A short piece of DNA, known as a hybridization probe , which has a nucleotide sequence complementary to a known sequence in the gene, is synthesized, and a radioactive phosphate group is added to it as a “tag.” You might be wondering how researchers are able to prepare such a probe if the gene has not yet been isolated. One way is to use a segment of the desired gene isolated from another organism. An alternative method depends on knowing all or part of the amino acid sequence of the protein produced by the gene of interest: the amino acid sequence is used to produce an approximate genetic code for the gene, and this nucleotide sequence is then produced synthetically. (The amino acid sequence used is carefully chosen to include, if possible, many amino acids such as methionine and tryptophan, which have only a single codon each.)
After a probe identifies a colony containing the desired gene, the DNA fragment is clipped out, again using restriction enzymes, and spliced into another replicating entity, usually a plasmid. Plasmids are tiny mini-chromosomes found in many bacteria, such as Escherichia coli ( E. coli ). A recombined plasmid would then be inserted into the host organism (usually the bacterium E. coli ), where it would go to work to produce the desired protein.
Proponents of recombinant DNA research are excited about its great potential benefits. An example is the production of human growth hormone, which is used to treat children who fail to grow properly. Formerly, human growth hormone was available only in tiny amounts obtained from cadavers. Now it is readily available through recombinant DNA technology. Another gene that has been cloned is the gene for epidermal growth factor, which stimulates the growth of skin cells and can be used to speed the healing of burns and other skin wounds. Recombinant techniques are also a powerful research tool, providing enormous aid to scientists as they map and sequence genes and determine the functions of different segments of an organism’s DNA.
In addition to advancements in the ongoing treatment of genetic diseases, recombinant DNA technology may actually lead to cures. When appropriate genes are successfully inserted into E. coli , the bacteria can become miniature pharmaceutical factories, producing great quantities of insulin for people with diabetes, clotting factor for people with hemophilia, missing enzymes, hormones, vitamins, antibodies, vaccines, and so on. Recent accomplishments include the production in E. coli of recombinant DNA molecules containing synthetic genes for tissue plasminogen activator, a clot-dissolving enzyme that can rescue heart attack victims, as well as the production of vaccines against hepatitis B (humans) and hoof-and-mouth disease (cattle).
Scientists have used other bacteria besides E. coli in gene-splicing experiments and also yeast and fungi. Plant molecular biologists use a bacterial plasmid to introduce genes for several foreign proteins (including animal proteins) into plants. The bacterium is Agrobacterium tumefaciens , which can cause tumors in many plants, but which can be treated so that its tumor-causing ability is eliminated. One practical application of its plasmids would be to enhance a plant’s nutritional value by transferring into it the gene necessary for the synthesis of an amino acid in which the plant is normally deficient (for example, transferring the gene for methionine synthesis into pinto beans, which normally do not synthesize high levels of methionine).
Restriction enzymes have been isolated from a number of bacteria and are named after the bacterium of origin. EcoRI is a restriction enzyme obtained from the R strain of E. coli . The roman numeral I indicates that it was the first restriction enzyme obtained from this strain of bacteria.
Summary
- The nucleotide sequence in DNA may be modified either spontaneously or from exposure to heat, radiation, or certain chemicals and can lead to mutations.
- Mutagens are the chemical or physical agents that cause mutations.
- Genetic diseases are hereditary diseases that occur because of a mutation in a critical gene.


16.8: The Pancreas
In most animals the pancreas is an oblong, pinkish organ that lies in the first bend of the small intestine (see diagram 16.7). In rodents and rabbits, however, it is spread thinly through the mesentery and is sometimes difficult to see.
Diagram 16.7 - The pancreas
Most of the pancreas acts as an exocrine gland producing digestive enzymes that are secreted into the small intestine. The endocrine part of the organ consists of small clusters of cells (called Islets of Langerhans ) that secrete the hormone insulin . This hormone regulates the amount of glucose in the blood by increasing the rate at which glucose is converted to glycogen in the liver and the movement of glucose from the blood into cells.
In diabetes mellitus the pancreas produces insufficient insulin and glucose levels in the blood can increase to a dangerous level. A major symptom of this condition is glucose in the urine.


<IP_ADDRESS>: Living Room Cleaning Tasks
The living room is often a place family spends a great deal of time. It should always appear tidy and organized. Home Health Aides/Personal Care Aides can encourage the family to pick up after themselves by modeling this behavior.
Living room tasks :
- Pick up clutter as you see it and at least once per day. Encourage and teach family members to do the same.
- Pick up newspapers, magazines, books, and toys as needed and at least once per day.
- Organize items kept in the living room and store them in their appropriate places.
- Vacuum rugs at least once per week. If there is dirt or food crumbs on the floor, you may need to vacuum more frequently. Crumbs from food attract pests.
- Sweep tile or linoleum floors daily. Mop at least once per week and more if floors are dirty.Always ensure a floor is dry after mopping to prevent falls.
- Dust surfaces once per week or more as required. You can use disposable dust cloths, dusting spray, or rags to remove dust.
- Ensure there are no loose rugs and other trip hazards, such as cords, in order to prevent falls.
- Lamps and lighting sources should be checked for good use. Good lighting helps to prevent falls.


7.19C: Riboswitches
- Describe riboswitches
Riboswitches are specific components of an mRNA molecule that regulates gene expression. The riboswitch is a part of an mRNA molecule that can bind and target small target molecules. An mRNA molecule may contain a riboswitch that directly regulates its own expression. The riboswitch displays the ability to regulate RNA by responding to concentrations of its target molecule. The riboswitches are naturally occurring RNA molecules that allow for RNA regulation. Hence, the existence of RNA molecules provide evidence to the RNA world hypothesis that RNA molecules were the original molecules, and that proteins developed later in evolution.
Riboswitches are found in bacteria, plants, and certain types of fungi. The various mechanisms by which riboswitches function can be divided into two major parts including an aptamer and an expression platform. The aptamer is characterized by the ability of the riboswitch to directly bind to its target molecule. The binding of the aptamer to the target molecule results in a conformational change of the expression platform, thus affecting gene expression. The expression platforms, which control gene expression, can either be turned off or activated depending on the specific function of the small molecule. Various mechanisms by which riboswitches function include, but are not limited to the following:
- The ability to function as a ribozyme and cleave itself if a sufficient concentration of its metabolite is present
- The ability to fold the mRNA in such a way the ribosomal binding site is inaccessible and prevents translation from occurring
- The ability to affect the splicing of the pre-mRNA molecule
The riboswitch, dependent on its specific function, can either inhibit or activate gene expression.
Key Points
- The mechanisms by which riboswitches regulate RNA expression, can be divided into two major processes, including aptamer and expression platform.
- The aptamer is characterized by the direct binding of the small molecule to its target.
- The expression platform is characterized by the conformational change, which occurs in the target upon binding of an aptamer, resulting in either inhibition or activation of gene expression.
Key Terms
- aptamer : Any nucleic acid or protein that is used to bind to a specific target molecule.


8.9: Displacement Current and Ampere’s Law
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In this section, we generalize Ampere’s Law, previously encountered as a principle of magnetostatics in Sections 7.4 and 7.9. Ampere’s Law states that the current \(I_{encl}\) flowing through closed path \(\mathcal{C}\) is equal to the line integral of the magnetic field intensity \({\bf H}\) along \(\mathcal{C}\). That is: \[\oint_{\mathcal{C}}{ {\bf H} \cdot d{\bf l} } = I_{encl} \label{m0053_fACLI} \] We shall now demonstrate that this equation is unreliable if the current is not steady; i.e., not DC.
First, consider the situation shown in Figure \(\PageIndex{1}\). Here, a current \(I\) flows in the wire, subsequently generating a magnetic field \({\bf H}\) that circulates around the wire (Section 7.5). When we perform the integration in Ampere’s Law along any path \(\mathcal{C}\) enclosing the wire, the result is \(I\), as expected. In this case, Ampere’s Law is working even when \(I\) is time-varying.
Figure \(\PageIndex{1}\): Ampere's Law applied to a continuous line of current (modified; C. Burks)Now consider the situation shown in Figure \(\PageIndex{2}\), in which we have introduced a parallel-plate capacitor. In the DC case, this situation is simple. No current flows, so there is no magnetic field and Ampere’s Law is trivially true. In the AC case, the current \(I\) can be non-zero, but we must be clear about the physical origin of this current. What is happening is that for one half of a period, a source elsewhere in the circuit is moving positive charge to one side of the capacitor and negative charge to the other side. For the other half-period, the source is exchanging the charge, so that negative charge appears on the previously positively-charged side and vice-versa. Note that at no point is current flowing directly from one side of the capacitor to the other; instead, all current must flow through the circuit in order to arrive at the other plate. Even though there is no current between the plates, there is current in the wire, and therefore there is also a magnetic field associated with that current.
Figure \(\PageIndex{1}\): Ampere's Law applied to a parallel plate capacitor (modified; C. Burks)Now we are ready to shine a light on the problem. Recall that from Stokes’ Theorem, the line integral over \({\mathcal C}\) is mathematically equivalent to an integral over any open surface \({\mathcal S}\) that is bounded by \({\mathcal C}\). Two such surfaces are shown in Figure \(\PageIndex{1}\) and Figure \(\PageIndex{2}\), indicated as \({\mathcal S}_1\) and \({\mathcal S}_2\). In the wire-only scenario of Figure \(\PageIndex{1}\), the choice of \({\mathcal S}\) clearly doesn’t matter; any valid surface intersects current equal to \(I\). Similarly in the scenario of Figure \(\PageIndex{2}\), everything seems fine if we choose \({\mathcal S}={\mathcal S}_1\). If, on the other hand, we select \({\mathcal S}_2\) in the parallel-plate capacitor case, then we have a problem. There is no current flowing through \({\mathcal S}_2\), so the right side of Equation \ref{m0053_fACLI} is zero even though the left side is potentially non-zero. So, it appears that something necessary for the time-varying case is missing from Equation \ref{m0053_fACLI}.
To resolve the problem, we postulate an additional term in Ampere’s Law that is non-zero in the above scenario. Specifically, we propose:
\[\oint_{\mathcal{C}}{ {\bf H} \cdot d{\bf l} } = I_c + I_d \nonumber \]
where \(I_c\) is the enclosed current (formerly identified as \(I_{encl}\)) and \(I_d\) is the proposed new term. If we are to accept this postulate, then here is a list of things we know about \(I_d\):
- \(I_d\) has units of current (A).
- \(I_d=0\) in the DC case and is potentially non-zero in the AC case. This implies that \(I_d\) is the time derivative of some other quantity.
- \(I_d\) must be somehow related to the electric field.
How do we know \(I_d\) must be related to the electric field? This is because the Maxwell-Faraday Equation tells us that spatial derivatives of \({\bf E}\) are related to time derivatives of \({\bf H}\); i.e., \({\bf E}\) and \({\bf H}\) are coupled in the time-varying (here, AC) case. This coupling between \({\bf E}\) and \({\bf H}\) must also be at work here, but we have not yet seen \({\bf E}\) play a role. This is pretty strong evidence that \(I_d\) depends on the electric field.
Without further ado, here’s \(I_d\):
\[I_d = \int_{\mathcal{S}} { \frac{\partial {\bf D}}{\partial t} \cdot d{\bf s} } \nonumber \]
where \({\bf D}\) is the electric flux density (units of C/m\(^2\)) and is equal to \(\epsilon{\bf E}\) as usual, and \(\mathcal{S}\) is the same open surface associated with \(\mathcal{C}\) in Ampere’s Law. Note that this expression meets our expectations: It is determined by the electric field, it is zero when the electric field is constant (i.e., not time varying), and has units of current.
The quantity \(I_d\) is commonly known as displacement current . It should be noted that this name is a bit misleading, since \(I_d\) is not a current in the conventional sense. Certainly, it is not a conduction current – conduction current is represented by \(I_c\), and there is no current conducted through an ideal capacitor. It is not unreasonable to think of \(I_d\) as current in a more general sense, for the following reason. At one instant, charge is distributed one way and at another, it is distributed in another way. If you define current as a time variation in the charge distribution relative to \(\mathcal{S}\) – regardless of the path taken by the charge – then \(I_d\) is a current. However, this distinction is a bit philosophical, so it may be less confusing to interpret “displacement current” instead as a separate electromagnetic quantity that just happens to have units of current.
Now we are able to write the general form of Ampere’s Law that applies even when sources are time-varying. Here it is:
\[\boxed{ \oint_{\mathcal{C}}{ {\bf H} \cdot d{\bf l} } = I_c + \int_{\mathcal{S}} { \frac{\partial {\bf D}}{\partial t} \cdot d{\bf s} } } \label{m0053_eACLI} \]
As is the case in the Maxwell-Faraday Equation, most of the utility of Ampere’s Law is unleashed when expressed in differential form. To obtain this form the first step is to write \(I_c\) as an integral of over \(\mathcal{S}\); this is simply (see Section 6.2): \[I_c = \int_{\mathcal{S}} {\bf J} \cdot d{\bf s} \nonumber \] where \({\bf J}\) is the volume current density (units of A/m\(^2\)). So now we have
\begin{aligned}
\oint_{C} \mathbf{H} \cdot d \mathbf{l} &=\int_{\mathcal{S}} \mathbf{J} \cdot d \mathbf{s}+\int_{S} \frac{\partial \mathbf{D}}{\partial t} \cdot d \mathbf{s} \\
&=\int_{\mathcal{S}}\left(\mathbf{J}+\frac{\partial \mathbf{D}}{\partial t}\right) \cdot d \mathbf{s}
\end{aligned}
We can transform the left side of the above equation into a integral over \(\mathcal{S}\) using Stokes’ Theorem. We obtain
\[\int_{\mathcal{S}} { \left( \nabla \times {\bf H} \right) \cdot d{\bf s} } = \int_{\mathcal{S}} { \left({\bf J}+ \frac{\partial {\bf D}}{\partial t} \right) \cdot d{\bf s} } \nonumber \]
The surface \(\mathcal{S}\) on both sides is the same, and we have not constrained \(\mathcal{S}\) in any way. \(\mathcal{S}\) can be any mathematically-valid open surface anywhere in space, having any size and any orientation. The only way the above expression can be universally true under these conditions is if the integrands on each side are equal at every point in space. Therefore:
\[\boxed{ \nabla \times {\bf H} = {\bf J} + \frac{\partial}{\partial t}{\bf D} } \label{m0053_eACLD} \]
which is Ampere’s Law in differential form.
What does Equation \ref{m0053_eACLD} mean? Recall that the curl of \({\bf H}\) is a way to describe the direction and rate of change of \({\bf H}\) with position. Therefore, this equation constrains spatial derivatives of \({\bf H}\) to be simply related to \({\bf J}\) and the time derivative of \({\bf D}\) (displacement current). Said plainly:
The differential form of the general (time-varying) form of Ampere’s Law (Equation \ref{m0053_eACLD}) relates the change in the magnetic field with position to the change in the electric field with time, plus current.
As is the case in the Maxwell-Faraday Equation, we see that electric and magnetic fields become coupled at each point in space when sources are time-varying.


7.8: Graphing Linear Inequalities in Two Variables
Location of Solutions
In our study of linear equations in two variables, we observed that all the solutions to the equation, and only the solutions to the equation, were located on the graph of the equation. We now wish to determine the location of the solutions to linear inequalities in two variables. Linear inequalities in two variables are inequalities of the forms:
\(\begin{aligned}
ax + by \le c & ax + by \ge c\\
ax + by < c & ax + by > c
\end{aligned}\)
A straight line drawn through the plane divides the plan into two half-planes
The straight line is called the boundary line.
Solution to an Inequality in Two Variables
Recall that when working with linear equations in two variables, we observed that ordered pairs that produced true statements when substituted into an equation were called solutions to that equation. We can make a similar statement for inequalities in two variables. We say that an inequality in two variables has a solution when a pair of values has been found such that when these values are substituted into the inequality a true statement results.
The Location of Solutions in the Plane
As with equations, solutions to linear inequalities have particular locations in the plane. All solutions to a linear inequality in two variables are located in one and only in one entire half-plane. For example, consider the inequality
\(2x + 3y \le 6\)
All solutions to the inequality \(2x + 3y \le 6\) lie in the shaded half-plane.
Point \(A(1, -1)\) is a solution since:
\(\begin{aligned}
2x + 3y \le 6\\
2(1) + 3(-1) \le 6?\\
2 - 3 \le 6?
-1 \le 6. \text{True.}
\end{aligned}\)
Point \(B(2, 5)\) is not a solution since:
\(\begin{aligned}
2x + 3y \le 6\\
2(2) + 3(5) \le 6?\\
4 + 15 \le 6?
19 \le 6. \text{False}
\end{aligned}\)
Method of Graphing
The method of graphing linear inequalities in two variables is as follows:
-
Graph the boundary line (consider the inequality as an equation, that is, replace the inequality sign with an equal sign).
- If the inequality is \(≤\) or \(≥\), draw the boundary line solid . This means that points on the line are solutions and are part of the graph.
- If the inequality is \(<\) or \(>\), draw the boundary line dotted . This means that points on the line are not solutions and are not part of the graph.
-
Determine which half-plane to shade by choosing a test point.
- If, when substituted, the test point yields a true statement, shade the half-plane containing it.
- If, when substituted, the test point yields a false statement, shade the half-plane on the opposite side of the boundary line.
Sample Set A
Graph \(3x - 2y \ge -4\).
1. Graph the boundary line. The inequality is \(\ge\) so we'll draw the line solid . Consider the inequality as an equation.
\(3x - 2y = -4\)
| \(x\) | \(y\) | \((x, y)\) |
|
\(0\) \(\dfrac{-4}{3}\) |
\(2\) \(0\) |
\((0, 2)\) (\(frac{-4}{3}, 0)\) |
2. Choose a test point. The easiest one is \((0, 0)\). Substitute \((0, 0)\) into the original inequality.
\(\begin{array}{flushleft}
3x - 2y \ge -4\\
3(0) - 2(0) \ge -4?\\
0 - 0 \ge -4?
0 \ge -4. \text{ True}
\end{array}\)
Shade the half-plane containing \((0, 0)\).
Graph \(x + y - 3 < 0\)
1. Graph the boundary line: \(x + y - 3 = 0\). The inequality is \( < \) so we'll draw the line dotted.
2. Choose a test point, say \((0, 0)\).
\(\begin{array}{flushleft}
x + y - 3 < 0\\
0 + 0 - 3 < 0?\\
-3 < 0. \text{ True}
\end{array}\)
Graph \(y \le 2x\).
1. Graph the boundary line \(y = 2x\). The inequality is \(\le\), so we'll draw the line solid .
2. Choose a test point, say \((0, 0)\).
\(\begin{array}{flushleft}
y \le 2x\\
0 \le 2(0)?\\
0 \le 0. \text{ True}
\end{array}\)
Shade the half-plane containing \((0, 0)\). We can't! \((0, 0)\) is right on the line! Pick another test point, say \((1, 6)\).
\(\begin{array}{flushleft}
y \le 2x\\
6 \le 2(1)\\
6 \le 2. \text{ False}
\end{array}\)
Shade the half-plane on the opposite side of the boundary line.
Graph \(y > 2\).
1. Graph the boundary line \(y = 2\). The inequality is \( >\) so we'll draw the line dotted.
2. We don't really need a test point. Where is \(y > 2\)? Above the line \(y = 2\)! Any point above the line clearly has a \(y\)-coordinate greater than \(2\)
Practice Set A
Solve the following inequalities by graphing.
\(-3x + 2y \le 4\)
- Answer
-
\(x−4y<4\)
- Answer
-
\(3x+y>0\)
- Answer
-
\(x≥1\)
- Answer
-
Exercises
Solve the inequalities by graphing.
\(y<x+1\)
- Answer
-
\(x+y≤1\)
\(−x+2y+4≥0\)
- Answer
-
\(−x+5y−10<0\)
\(−3x+4y>−12\)
- Answer
-
\(2x+5y−15≥0\)
\(y≤4\)
- Answer
-
\(x≥2\)
\(x≤0\)
- Answer
-
\(x−y<0\)
\(x+3y≥0\)
- Answer
-
\(−2x+4y>0\)
Exercises for Review
Graph the inequality \(−3x+5≥−1\).
- Answer
-
Supply the missing word. The geometric representation (picture) of the solutions to an equation is called the of the equation.
Supply the denominator: \(m = \dfrac{y_2-y_1}{?}\)
- Answer
-
\(m = \dfrac{y_2-y_1}{x_2-x_1}\)
Graph the equation \(y=−3x+2\).
Write the equation of the line that has slope \(4\) and passes through the point \((−1, 2)\).
- Answer
-
\(y=4x+6\)


1.4: Sources of Law
Where does law come from? How do individuals and businesses know right from wrong? Not all actions that are considered “wrong” or inappropriate are violations of the law. They simply may represent social norms. So what is the difference? There are two types of rules in our society—social norms and laws.
Social norms are the informal rules that govern behavior in groups and societies. Social norms and cultural expectations may be violated with negative social or professional consequences for doing so. However, no legal repercussions follow violating social norms alone.
Violations of law are different. Violating the law carries penalties, such as civil liability, fines, or loss of liberty. While it is optional to conform to social customs, people are compelled to obey the law under threat of penalty.
Laws are generally classified as public law or private law. Public law applies to everyone. It is law that has been created by a legitimate authority with the power to create law, and it applies to the people within its jurisdiction. In the United States, the lawmaking authority itself is also subject to those laws, because no one is “above” the law. If the law is violated, penalties may be levied against violators. Examples of public law include constitutions, criminal laws, and administrative laws. For example, if someone steals items from a store, the thief is violating public law. He committed the crime of theft which affects the community as a whole (not just the store owners), and the crime is defined in public legislation.
Private law is law that is binding on specific parties. For instance, parties to a contract are involved in a private law agreement. The terms of the contract apply to the parties of the contract but not anyone else. If the parties have a contract dispute, the terms of the contract and the remedy for breach will apply only to the parties of the contract. In addition to contracts, other examples of private law include tort and property laws. For example, if someone installs an industrial smoker on his property and the smoke creates a dense haze in the neighbor’s yard, there may be a violation of private law because the smoke is interfering with the neighbor’s right to peacefully enjoy one’s property.
Laws are also classified as civil or criminal. Civil law is usually brought by a private party against another private party. For example, one company decides to sue another for breach of contract. Or a customer sues a business when injured by the company’s product. Most laws affecting businesses are civil.
Criminal law involves a governmental decision to prosecute someone for violating a criminal statute. If someone breaks a criminal law, he or she could lose their freedom (i.e. be sent to prison) or lose their life (i.e. if convicted of a capital offense). In a civil action, no one is sent to prison. Usually, liability results in the loss of property such as money or assets.
| Civil | Criminal | |
| Source of Law | statute or common law | statutes defining crimes |
| Who files case? | business or individual suffering harm | the government (e.g. District Attorney) |
| Burden of Proof | preponderance of evidence | beyond a reasonable doubt |
| Remedy | damages, injunction, specific performance | punishment (e.g. fine or imprisonment) |
| Purpose | provide compensation or private relief | protect society |
Additionally, some law is procedural and some law is substantive. Procedural law describes the legal process and rules that are required and must be followed. For instance, parties who are sued in court must receive notice of the lawsuit before the court can impose judgment against them. Substantive law refers to the actual substance of the law or the merits of the claim, case, or action. Substantive law embodies the ideas of legal rights and duties and is captured by different sources of law, including the Constitution, statutes, and common law.
For example, if someone drives fifty-five miles per hour in a forty mile-per-hour zone, she has broken the substantive rule of law of the speed limit. However, how and what gets decided in court related to the speeding ticket is a matter of procedural law. For example, whether the driver is entitled to a hearing before a judge, whether she has a right to be represented by legal counsel, whether the hearing takes place within a certain amount of time after the ticket was issued, and what type of evidence can be presented are procedural law issues.
Sources of Law
In the United States, our laws come primarily from:
- Federal and state constitutions;
- Statutory law from Congress, the state legislatures, and local legislative bodies;
- Common law from federal and state appellate courts;
- Administrative rules and regulations;
- Treaties and conventions; and
- Executive orders.
Constitutions
The most fundamental law in the United States is the US Constitution, which is the supreme law of the nation. Any law that conflicts with it is void. The Constitution serves three important functions. First, it establishes the structure of our national government and identifies the powers of the legislative, executive, and judicial branches. Second, it defines the boundaries of each branch’s authority and creates “checks” on each branch by the other branches. For example, the president is the commander-in-chief of the armed forces, but does not have the power to declare war. That duty falls to Congress. And, third, the Constitution guarantees civil liberties and individual rights.
The power granted to the federal government by the Constitution is limited. Any powers not expressly granted to the federal government by the Constitution are reserved to the states. This means that if the Constitution does not give the federal government power over a particular area, then the states regulate it.
The first ten amendments to the Constitution are known as the Bill of Rights . Despite the limited power granted to the federal government by the Constitution, the Bill of Rights protects certain individual civil rights and liberties from governmental interference. These rights include the freedom of speech and religion, the right to bear arms, and the rights of individuals who are suspected and accused of crimes.
Figure 1.2 Separation of Powers of the Federal Government
Each state also has its own constitution, which serves essentially the same function for the state government as the US Constitution serves for the federal government. Specifically, they establish limits of state government power, establish the organization and duties of the different branches of government at the state level, and protect fundamental rights of state citizens. This dual system of government in the United States is called federalism , which is a governance structure whereby the federal government and the state governments coexist through a shared power scheme.
Figure 1.3 Separation of Powers of the State Governments
Statutes
Statutes are laws created by a legislative body. Congress is the federal legislative body, and each state also has its own legislative body. Almost all statutes are created by the same method. An idea for a new law is proposed in the legislature. This proposal is called a bill . The House of Representatives and Senate independently vote on a bill. If the majority of both chambers approves it, the bill is sent to the president or governor for approval. If the president or governor signs the bill, then it becomes a statute.
Local governments, such as counties, cities, and townships, may be authorized under a state constitution to create or adopt ordinances. An ordinance is a legislative act of a local government entity. Examples of ordinances include building codes, zoning laws, and misdemeanors such as jaywalking.
Common Law
Binding legal principles also come from the courts. When appellate courts decide a case, they may interpret and apply legal principles in a way that are binding on lower courts in the future. The process of applying a prior appellate decision to a case is called precedent . Simply put, precedent is when judges use past decisions to guide them. The benefit of precedent is that it makes the law predictable and furthers the rule of law by applying legal principles to the greater community, not just the parties to a lawsuit. Businesses value common law systems because they reduce the cost of business. For example, if a business is unsure of how its contract rights will be applied by the court, it can understand its rights by learning how courts interpreted similar contract provisions in past lawsuits. This allows businesses to assess their risks, determine their liability, and make rational business decisions without the expense of litigation.
Administrative Rules and Regulations
Administrative law is the collection of rules and decisions made by agencies to fill in particular details missing from constitutions and statutes. For example, the Internal Revenue Service (IRS) is the federal agency responsible for collecting national taxes and administering the Internal Revenue Code enacted by Congress. All businesses and individuals must follow the IRS rules and regulations about how to report, file, and pay applicable taxes that Congress levies. Congress passes statute defining “what” taxes need to be paid. The IRS adopts the rules about “how” those taxes are paid.
In the United States, many of the day-to-day regulation of businesses is done by administrative agencies. These agencies are created by the legislature to implement and enforce a particular statute. Agencies often report to the executive branch, but some are run by independent commissions. Legislative bodies give agencies the power to create rules and regulations that individuals and businesses must follow to comply with the statute. For example, the Environmental Protection Agency (EPA) was created to implement and enforce the Clean Air Act and the Clean Water Act.
Treaties and Conventions
A treaty is a binding agreement between two nations. A convention is a binding agreement among a group of nations. In the US, a treaty or convention is generally negotiated by the executive branch. To be binding, the US Constitution requires the Senate to ratify treaties by a two-thirds vote. Once ratified, a treaty becomes part of federal law with the same weight and effect as a statute passed by the entire Congress. Therefore, treaties and conventions have equal standing as statutes in US law.
Executive Orders
Article II, Section 1 of the US Constitution gives the president the power to “take care that the laws be faithfully executed.” Under this power, the president may issue executive orders requiring officials in the executive branch to perform their duties in a particular manner. State governors have the same authority under state constitutions. Although they are not laws that apply directly to individuals and businesses, executive orders are important legal documents because they direct the government’s enforcement efforts.
Hierarchy of Sources of Law
| Priority | Source | Comment |
| 1 | Constitutions | Exist at both federal and state levels |
| 2 (tie) | Statutes | Laws passed by the federal or state legislatures |
| 2 (tie) | Treaties and Conventions | International agreements that have the same standing as statutes |
| 4 | Judicial Opinions | Court interpretation and application of constitutions, statutes, treaties, agency regulations, and executive orders |
| 5 | Agency Regulations | Rules and regulations adopted by administrative agencies at the federal, state, or local level |
| 6 | Executive Orders | Guidance from the president or governor to executive branch officials about how to perform their duty |


15.3: September 11 and the War on Terror
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On the morning of September 11, 2001, nineteen operatives of the al-Qaeda terrorist organization hijacked four passenger planes on the East Coast. American Airlines Flight 11 crashed into the North Tower of the World Trade Center in New York City at 8:46 a.m. Eastern Daylight Time (EDT). United Airlines Flight 175 crashed into the South Tower at 9:03. American Airlines Flight 77 crashed into the western façade of the Pentagon at 9:37. At 9:59, the South Tower of the World Trade Center collapsed. At 10:03, United Airlines Flight 93 crashed in a field outside Shanksville, Pennsylvania, brought down by passengers who had received news of the earlier hijackings. At 10:28, the North Tower collapsed. In less than two hours, nearly three thousand Americans had been killed.
The attacks stunned Americans. Late that night, Bush addressed the nation and assured the country that “the search is under way for those who are behind these evil acts.” At Ground Zero three days later, Bush thanked first responders for their work. A worker said he couldn’t hear him. “I can hear you,” Bush shouted back, “The rest of the world hears you. And the people who knocked these buildings down will hear all of us soon.”
American intelligence agencies quickly identified the radical Islamic militant group al-Qaeda, led by the wealthy Saudi Osama bin Laden, as the perpetrators of the attack. Sheltered in Afghanistan by the Taliban, the country’s Islamic government, al-Qaeda was responsible for a 1993 bombing of the World Trade Center and a string of attacks at U.S. embassies and military bases across the world. Bin Laden’s Islamic radicalism and his anti-American aggression attracted supporters across the region and, by 2001, al-Qaeda was active in over sixty countries.
Although in his presidential campaign Bush had denounced foreign nation-building, he populated his administration with neoconservatives, firm believers in the expansion of American democracy and American interests abroad. Bush advanced what was sometimes called the Bush Doctrine, a policy in which the United States would have the right to unilaterally and preemptively make war on any regime or terrorist organization that posed a threat to the United States or to U.S. citizens. It would lead the United States into protracted conflicts in Afghanistan and Iraq and entangle the United States in nations across the world. Journalist Dexter Filkins called it a Forever War, a perpetual conflict waged against an amorphous and undefeatable enemy. 16 The geopolitical realities of the twenty-first-century world were forever transformed.
The United States, of course, had a history in Afghanistan. When the Soviet Union invaded Afghanistan in December 1979 to quell an insurrection that threatened to topple Kabul’s communist government, the United States financed and armed anti-Soviet insurgents, the Mujahideen. In 1981, the Reagan administration authorized the CIA to provide the Mujahideen with weapons and training to strengthen the insurgency. An independent wealthy young Saudi, Osama bin Laden, also fought with and funded the Mujahideen. And they began to win. Afghanistan bled the Soviet Union dry. The costs of the war, coupled with growing instability at home, convinced the Soviets to withdraw from Afghanistan in 1989. 17
Osama bin Laden relocated al-Qaeda to Afghanistan after the country fell to the Taliban in 1996. Under Bill Clinton, the United States launched cruise missiles at al-Qaeda camps in Afghanistan in retaliation for al-Qaeda bombings on American embassies in Africa.
After September 11, with a broad authorization of military force, Bush administration officials made plans for military action against al-Qaeda and the Taliban. What would become the longest war in American history began with the launching of Operation Enduring Freedom in October 2001. Air and missile strikes hit targets across Afghanistan. U.S. Special Forces joined with fighters in the anti-Taliban Northern Alliance. Major Afghan cities fell in quick succession. The capital, Kabul, fell on November 13. Bin Laden and al-Qaeda operatives retreated into the rugged mountains along the border of Pakistan in eastern Afghanistan. The American occupation of Afghanistan continued.
As American troops struggled to contain the Taliban in Afghanistan, the Bush administration set its sights on Iraq. After the conclusion of the Gulf War in 1991, American officials established economic sanctions, weapons inspections, and no-fly zones. By mid-1991, American warplanes were routinely patrolling Iraqi skies and coming under periodic fire from Iraqi missile batteries. The overall cost to the United States of maintaining the two no-fly zones over Iraq was roughly $1 billion a year. Related military activities in the region added almost another $500 million to the annual bill. On the ground in Iraq, meanwhile, Iraqi authorities clashed with UN weapons inspectors. Iraq had suspended its program for weapons of mass destruction, but Saddam Hussein fostered ambiguity about the weapons in the minds of regional leaders to forestall any possible attacks against Iraq.
In 1998, a standoff between Hussein and the United Nations over weapons inspections led President Bill Clinton to launch punitive strikes aimed at debilitating what was thought to be a developed chemical weapons program. Attacks began on December 16, 1998. More than two hundred cruise missiles fired from U.S. Navy warships and Air Force B-52 bombers flew into Iraq, targeting suspected chemical weapons storage facilities, missile batteries, and command centers. Airstrikes continued for three more days, unleashing in total 415 cruise missiles and 600 bombs against 97 targets. The number of bombs dropped was nearly double the number used in the 1991 conflict.
The United States and Iraq remained at odds throughout the 1990s and early 2000, when Bush administration officials began championing “regime change.” The Bush administration publicly denounced Saddam Hussein’s regime and its alleged weapons of mass destruction. It began pushing for war in the fall of 2002. The administration alleged that Hussein was trying to acquire uranium and that it had aluminum tubes used for nuclear centrifuges. Public opinion was divided. George W. Bush said in October, “Facing clear evidence of peril, we cannot wait for the final proof—the smoking gun—that could come in the form of a mushroom cloud.” 18 The administration’s push for war was in full swing. Protests broke out across the country and all over the world, but majorities of Americans supported military action. On October 16, Congress passed the Authorization for Use of Military Force Against Iraq resolution, giving Bush the power to make war in Iraq. Iraq began cooperating with UN weapons inspectors in late 2002, but the Bush administration pressed on. On February 6, 2003, Secretary of State Colin Powell, who had risen to public prominence as chairman of the Joint Chiefs of State during the Persian Gulf War in 1991, presented allegations of a robust Iraqi weapons program to the UN. Protests continued.
The first American bombs hit Baghdad on March 20, 2003. Several hundred thousand troops moved into Iraq and Hussein’s regime quickly collapsed. Baghdad fell on April 9. On May 1, 2003, aboard the USS Abraham Lincoln , beneath a banner reading Mission Accomplished , George W. Bush announced that “major combat operations in Iraq have ended.” 19 No evidence of weapons of mass destruction were ever found. And combat operations had not ended, not really. The Iraqi insurgency had begun, and the United States would spend the next ten years struggling to contain it.
Efforts by various intelligence gathering agencies led to the capture of Saddam Hussein, hidden in an underground compartment near his hometown, on December 13, 2003. The new Iraqi government found him guilty of crimes against humanity and he was hanged on December 30, 2006.


2.19: Axillary Temperature
The normal axillary temperature may be as much as 1ºC lower than the oral temperature (OER #1). An axillary thermometer is the same electronic device as an oral thermometer, and both have a blue end.
Technique
Remove the probe from the device and place a probe cover (from the box) on the thermometer without touching the cover with your hands. Ask the client to raise the arm away from his/her body. Place the thermometer in the client’s armpit (OER #1), on bare skin, as high up into the axilla as possible, with the point facing behind the client. Ask the client to lower his/her arm and leave the device in place for as long as is indicated by the device manufacturer (OER #1). Usually the device beeps in 10–20 seconds. Discard the probe cover in the garbage (without touching the cover) and place the probe back into the device. See Figure 2.6 of an axillary temperature being taken.
Figure 2.6: Axillary temperature being taken
What should the healthcare provider consider?
The axillary route is a minimally invasive way to measure temperature. It is commonly used in children. It is important to ensure that the thermometer is as high up in the axilla as possible with full skin contact and that the client’s arm is then lowered down.
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Part of this content was adapted from OER #1 (as noted in brackets above):
© 2015 British Columbia Institute of Technology (BCIT). Clinical Procedures for Safer Patient Care by Glynda Rees Doyle and Jodie Anita McCutcheon, British Columbia Institute of Technology. Licensed under a Creative Commons Attribution 4.0 International License , except where otherwise noted. Download this book for free at http://open.bccampus.ca