6.3: Post-Lab 6 Questions
(2 points)
Last Name: _______________________ First Name: _______________________
1) Write a C if the listed structure is part of the conducting zone and an R if it is part of the respiratory zone. Also, label whether the structure is part of the upper respiratory ( U ) or lower respiratory system ( L ). (0.5 point)
Example: Larynx C , L
Alveoli ________________
Trachea ________________
Nasal cavity ________________
Bronchi ________________
Respiratory bronchioles ________________
Pharynx ________________
Alveolar ducts ________________
Terminal bronchioles ________________
2) Write the route that oxygen takes from when you inhale to the point of gas exchange with carbon dioxide. (0.5 point)
3) Give two unique characteristics of the pulmonary artery and vein. (0.5 point)
4) Describe the route of pulmonary circulation. (0.5 point)


7.1: How to draw the multivariate data
The most simple operation with multidimensional data is to draw it.
Pictographs
Pictograph is a plot where each element represents one of objects, and every feature of the element corresponds with one character of the primary object. If the every row of data is unique , pictographs might be useful. Here is the star plot (Figure \(\PageIndex{1}\)) example:
Code \(\PageIndex{1}\) (R):
(We made every element to represent the species of horsetails, and length of the particular ray corresponds with some morphological characters. It is easy to see, as an example, similarities between Equisetum \(\times\)litorale and E. fluviatile .)
Slightly more exotic pictograph is Chernoff’s faces where features of elements are shown as human face characters (Figure \(\PageIndex{1}\)):
Code \(\PageIndex{2}\) (R):
(Original Chernoff’s faces have been implemented in the faces2() function, there is also another variant in symbols() package.)
Related to pictographs are ways to overview the whole numeric dataset, matrix or data frame. First, command image() allows for plots like on Figure \(\PageIndex{3}\):
Code \(\PageIndex{3}\) (R):
(This is a “portrait” or iris matrix, not extremely informative but useful in many ways. For example, it is well visible that highest, most red, values of Pt.L (abbreviated from Petal.Length ) correspond with lowest values of Sp.W ( Sepal.Width ). It is possible even to spot 3-species structure of this data.)
More advanced is the parallel coordinates plot (Figure \(\PageIndex{4}\)):
Code \(\PageIndex{4}\) (R):
This is somewhat like the multidimensional stripchart. Every character is represented with one axis which has its values from all plants. Then, for every plant, these values were connected with lines. There are many interesting things which could be spotted from this plot. For example, it is clear that petal characters are more distinguishing than sepal. It is also visible that Iris setosa is more distinct from two other species, and so on.
Grouped plots
Even boxplots and dotcharts could represent multiple characters of multiple groups, but you will need to scale them first and then manually control positions of plotted elements, or use Boxplots() and Linechart() described in the previous chapter:
Code \(\PageIndex{5}\) (R):
(Please try these plots yourself.)
Function matplot() allows to place multiple scatterplots in one frame, symbols() allows to place multiple smaller plots in desired locations, and function pairs() allows to show multiple scatterplots as a matrix (Figure \(\PageIndex{5}\)).
Code \(\PageIndex{6}\) (R):
(This matrix plot shows dependencies between each possible pair of five variables simultaneously.)
Matrix plot is just one of the big variety of R trellis plots. Many of them are in the lattice package (Figure \(\PageIndex{6}\)):
Code \(\PageIndex{7}\) (R):
(Note how to use make.groups() and do.call() to stack all columns into the long variable (it is also possible to use stack() , see above). When LOC was added to temporary dataset, it was recycled five times—exactly what we need.)
Library lattice offers multiple trellis variants of common R plots. For example, one could make the trellis dotchart which will show differences between horsetail species (Figure \(\PageIndex{7}\))
Code \(\PageIndex{8}\) (R):
(Here we stacked all numerical columns into one with stack() .)
Few trellis plots are available in the core R . This is our election data from previous chapter (Figure \(\PageIndex{8}\)):
Code \(\PageIndex{9}\) (R):
3D plots
If there just three numerical variables, we can try to plot all of them with 3-axis plots. Frequently seen in geology, metallurgy and some other fields are ternary plots . They implemented, for example, in the vcd package. They use triangle coordinate system which allows to reflect simultaneously three measurement variables and some more categorical characters (via colors, point types etc .):
Code \(\PageIndex{10}\) (R):
The “brick” 3D plot could be done, for example, with the package scatterplot3d (Figure \(\PageIndex{10}\)):
Code \(\PageIndex{11}\) (R):
(Here some additional efforts were used to make y-axis label slanted.)
These 3D scatterplots look attractive, but what if some points were hidden from the view? How to rotate and find the best projection? Library RGL will help to create the dynamic 3D plot:
Code \(\PageIndex{12}\) (R):
Please run these commands yourself. The size of window and projection in RGL plots are controlled with mouse. That will help to understand better the position of every point. In case of iris data, it is visible clearly that one of the species ( Iris setosa ) is more distinct than two others, and the most “splitting” character is the length of petals ( Petal.Length ). There are four characters on the plot, because color was used to distinguish species. To save current RGL plot, you will need to run rgl.snapshot() or rgl.postscript() function. Please also note that RGL package depends on the external OpenGL library and therefore on some systems, additional installations might be required.
Another 3D possibility is cloud() from lattice package. It is a static plot with the relatively heavy code but important is that user can use different rotations (Figure 7.2.1):
Code \(\PageIndex{13}\) (R):


7.3: Nucleophilic Acyl Substitution Reactions
After completing this section, you should be able to
- compare the reactions of carboxylic acid derivatives with nucleophiles to the reactions of aldehydes and ketones with nucleophiles.
- arrange a given list of carboxylic acid derivatives in order of increasing or decreasing reactivity towards nucleophiles.
- explain the difference in reactivity towards nucleophiles of two or more given carboxylic acid derivatives.
- explain why esters and amides are commonly found in nature, but acid halides and acid anhydrides are not.
The reading describes the relative reactivities of “biologically relevant acyl groups.” Both acid anhydrides and acid halides readily react with water and cannot exist for any length of time in living organisms. The following scheme illustrates the relative reactivities of most carboxylic acid derivatives considering the R group to be the same for all of them.
Carboxylic acid derivatives and acyl groups
Carboxylic acid derivatives can be distinguished from aldehydes and ketones by the presence of a group containing an electronegative heteroatom - usually oxygen, nitrogen, sulfur or phosphorus – bonded directly to the carbonyl carbon and represented by the symbol Y . The rest of the carboxylic acid derivative is called the acyl group, which comprises the carbonyl group and the attached alkyl group (R).
Being electronegative, the Y group has the potential of receiving electrons from the alkoxide intermediate created during a nucleophilic acyl substitution and acting as a leaving group. Eliminating a leaving group allows carbonyl bond reformation and C-Y bond cleavage to complete a substitution reaction.
The stability of a negative charge on a Y group can be gauged by the pK a of its corresponding conjugate acid (HY). A low conjugate acid pK a implies that the Y leaving group is a weak base with a stable negative charge and thus would make an efficient leaving group. Likewise, a high conjugate acid pK a means the Y group would likely make a poor leaving group. As shown in the table below, the conjugate acids of the possible carbide (R: - ) and hydride (H: - ) leaving groups of aldehydes and ketones have a relatively high pK a , while those of the Y leaving groups of carboxylic acid derivatives are much lower. In fact, the stability of the leaving groups is an important factor in determining the reactivity of different carboxylic acid derivatives toward nucleophilic acyl substitutions. Based on the pK a data we can deduce that amides will most likely be the least reactive of the carboxylic acid derivatives.
Carbonyl Compounds and their Leaving Groups
| Nam e | Carbonyl Compound | Leaving Group | Conjugate Acid of the Leaving Group | pK a |
| Acid Chloride | Cl - | H-Cl | -7 | |
| Acid Anhydride | 3-5 | |||
| Ester | - OR' | H-OR' | 15-16 | |
| Carboxylic Acid | - OH | H-OH | 15.7 | |
| Amide | - NH 2 | H-NH 2 | 36 | |
| Ketone | - R' | H-R' | 50 | |
| Aldehyde | - H | H-H | Very Large |
What is the ‘Y’ group in:
a. an acid anhydride? b. a carboxylic acid?
- Answer
-
a. b.
The Mechanism of Nucleophilic Acyl Substitution
Aldehydes and ketones, along with carboxylic acid derivatives all have the C=O carbonyl bond in common. Thus, the electrophilic character of the carbonyl carbon plays an important part in the reactivity of all of these compounds. Because the carbonyl carbons of aldehydes and ketones do not contain suitable leaving groups, their primary reaction is fundamentally different than carboxylic acid derivatives.
Remember that aldehydes and ketones tend to undergo nucleophilic addition to form a tetrahedral alkoxide intermediate. Once formed, the negative charge of the alkoxide intermediate cannot be transferred to other substituents because the potential carbide (R: - ) and hydride (H: - ) leaving groups are too unstable. Instead the negative charge is held by the alkoxide until protonation converts it into an alcohol.
Carboxylic acid derivatives tend to undergo a reaction called nucleophilic acyl substitution. Similarly to nucleophilic addition, this mechanism starts with a nucleophilic attack on an electrophilic carbonyl carbon, forming a tetrahedral alkoxide intermediate. The alkoxide negative charge can gain stability by being transferred to the Y leaving group. Elimination of the Y leaving group in the second mechanistic step, allows the C=O carbonyl bond to reform thus creating a new acyl compound. The reaction is considered a substitution due to the Y group of the carboxylic acid derivative being exchanged with an incoming nucleophile.
| Step 1) Nucleophilic Addition | Step 2) Leaving Group Removal |
Show the mechanism of the following nucleophilic acyl substitution reaction, using curved arrows to indicate the electron flow in each step:
- Answer
-
The Relative Reactivity of Carboxylic Acid Derivatives
The relative reactivity of carboxylic acid derivatives is an important concept for entering into a detailed examination of nucleophilic acyl substitutions. There are two main concepts directly relating to the mechanism, which when combined lead to an overall explanation of the differences in reactivity: the stability of the carbonyl and the Y leaving group .
Carbonyl Stability
Both the initial addition step and the subsequent elimination step can affect the overall rate of a nucleophilic acyl substitution reaction, but the addition is usually the rate-limiting step. Thus, any factor that makes the carbonyl group more reactive toward nucleophiles favors the substitution process.
Steric and electronic factors are both important in determining reactivity. Sterically, we find within a series of similar acid derivatives that unhindered, accessible carbonyl groups react with nucleophiles more readily than do sterically hindered carbonyl groups. The reactivity order is
Electronically, any stabilization of the carbonyl moiety reduces the electrophilic character of the carbonyl carbon by reducing its partial positive charge, reducing the rate of this step of the mechanism. The ability of substituents attached to the carbonyl carbon to donate or withdraw electron density is the primary factor determining carbonyl stabilization. As previously discussed, the presence of two electron donating alkyl substituents reduces the partial positive charge on ketones' carbonyl carbon, making them less reactive to nucleophilic attack than aldehydes.
Additionally, the Y group heteroatom's ability to stabilize a carbonyl by donating electrons through resonance makes most carboxylic acid derivatives even less reactive. Thus, amides are the least reactive because the pair of electrons on the nitrogen atom provides electrons to the carbonyl carbon. Overall, delocalization of the carbonyl carbon's partial positive charge onto the adjacent Y group heteroatom reduces the electrophilic character of the carbonyl. The electronegativity of the Y group heteroatom generally determines extent of this stabilization. The less electronegative the Y group heteroatom, the better it is able to stabilize the resonance structure with the delocalized positive charge, reducing the carbonyl's electrophilicity.
As contrast, strongly polarized acyl compounds react more readily than less polar ones. Thus, acid chlorides are the most reactive because the electronegative chlorine atom withdraws electrons from the carbonyl carbon. Although subtle, electrostatic potential maps of various carboxylic acid derivatives indicate these differences by the relative blueness on the carbons. Acyl phosphates are hard to place on this scale because they are not often used in the laboratory, but in biological systems they appear to be somewhat more reactive than thioesters.
Leaving Group Ability
The leaving group ability of the Y group is the most important factor in determining the rate of the second mechanistic step of nucleophilic acyl substitution. As discussed above, the effectiveness of a leaving group is related to its ability to stabilize a negative charge particularly through having a relatively high electronegativity or having the ability to delocalize the negative charge through resonance. The Y group structural features which allow for the stabilization of a negative charge also allow for the stabilization of the transition state of the second step of the mechanism. Overall, the better the leaving group ability of the Y group, the higher the rate of second step of the mechanism.
These two effects, carbonyl stability and leaving group ability, when combined predict the relative reactivity of carboxylic acid derivatives. Fortunately, the effects tend to work synergistically. Y groups that are effective leaving groups also tend to poorly stabilize carbonyls through resonance making reaction rates of nucleophilic acyl substitution higher. Likewise, poor leaving groups tend to stabilize carbonyls through resonance and reduce reaction rates effectively. In fact, depending on the carbonyl structure, either step one or step two of the mechanism can be the rate-determining step. For Y groups with a poor leaving group ability, the second step of the mechanism is rate determining because of the weakly stabilized transition state. The first step of the mechanism is rate determining for Y groups with good leaving group ability because they tend to stabilize the starting material's carbonyl, increasing the energy distance to the first transition state.
How the two effects actually combine to produce the overall reactivity for each carboxylic acid derivative is slightly different. As comparison of one of the more reactive carboxylic acid derivatives, acid chlorides, and one of the least reactive, amides, will be used as a discussion.
In amides, the nitrogen atom is a powerful electron donating group by resonance. Nitrogen is less electronegative than oxygen and can therefore better stabilize the resonance structure of the delocalized positive charge than most other acid derivatives. This lowers the energy of the starting material which increases the overall energy barrier. Likewise, -NH 2 is a relatively poor leaving group (since it is the conjugate base of a very weak acid RNH 2 ) which increases the transition state energy of the second step of the mechanism also increasing the overall energy barrier. The two effects combine to increase the overall energy barrier which must be overcome during the reaction, causing reaction rates to decrease and making amides very unreactive toward nucleophilic acyl substitution.
In acid chlorides the -Cl is a very effective leaving group making the energy barrier of the second step relatively small. However, this does not have a significant effect since the first step of the mechanism is rate determining. The resonance stabilization offered by the chlorine atom is ineffective due to the poor overlap between the chlorine 3p orbital and the carbon 2p orbital. The poor overlap means that acid chlorides are much less stabilized by resonance than amides. In addition, since chlorine is more electronegative than nitrogen was in the amide example, the inductive electron-withdrawing effects of chlorine become important. This destabilizes the carbonyl and increases the electrophilic character of the carbonyl carbon. The energy barrier of the first step of the mechanism is small due to the lack of stabilization in the acid chloride starting material. Therefore the overall rate of reaction for acid chlorides is high making them very reactive towards nucleophilic acyl substitutions.
As a general rule, stabilizing effects from the Y heteroatom tends to make carboxylic acid derivatives less reactive toward the initial nucleophilic attack than aldehydes and ketone. One notable exception is acid chlorides, where the destabilizing inductive electron-withdrawing properties of the chlorine outweigh the resonance stabilizing effects making them more reactive towards nucleophilic attack. This point will become important later in the chapter where it will be used to explain the outcome of certain reactions.
The reactivity of a carboxylic acid derivative can be visualized by using an electrostatic potential map to look at the electron density around the carbonyl carbon. A blue/green color represents the amount of positive charge present. The carbonyl carbons of the amide and ester have a relatively small amount of positive charge making them among the least reactive toward nucleophilic attack. The acid chloride's and anhydride's carbonyl carbon has more of a blue/color color indicating a higher positive charge and making them more reactive than the amide and ester.
Rank the compounds in each of the following sets in order of their expected reactivity toward nucleophilic acyl substitution:
- Answer
-
- Acetyl chloride > Methyl acetate > Acetamide
- Hexafluoroisopropyl acetate > 2,2,2-Trichloroethyl acetate > Ethyl acetate
Acid Derivative Interconversion
From this understanding of reactivity, multiple step synthesis strategies can be developed. Typically more reactive carboxylic acid derivatives can be used to synthesize less reactive derivatives as illustrated in the diagram below. As will be shown later in this chapter, highly reactive acid chlorides, when combined with the appropriate nucleophile, can be directly converting into acid anhydrides, thioester, esters, and amides. However, the less reactive amides cannot be directly converted into ester, thioester, anhydrides, or acid chlorides. It is possible to make these conversions with an amide but multiple reaction steps are required.
The nucleophiles required to make the conversion from one carboxylic acid derivative to another are common and have been discussed multiple times in this text. Because the same nucleophile is typically used to convert to a specific carboxylic acid derivative conversion, the reactions are given generic names. (Figure \(\PageIndex{3}\)).
- Hydrolysis: A reaction with water as a nucleophile to create a carboxylic acid.
- Alcoholysis: A reaction with an alcohol nucleophile to create an ester.
- Aminolysis: A reaction with ammonia or an amine nucleophile to create an amide.
- Reduction: A reaction with a hydride nucleophile to create an aldehyde or 1 o alcohol.
- Organometallic (Grignard reaction): A reaction with a carbanion nucleophile from an organometallic reagent to create a ketone or a 3 o alcohol.
Predicting the Product of a Nucleophilic Acyl Substitution Reaction
There are two major pieces of a nucleophilic acyl substitution reaction which need to be identified in order to predict the product: the leaving group of the carboxylic acid derivative (Y) and the nucleophile. It is important to identify if the nucleophile is neutral (i.e. water, alcohols, ammonia, amines) or negatively charged (i.e. hydroxide, alkoxides, hydrides, carbanions). Also, it is important to note that certain hydride and organometallic reagents are capable of a double addition to carboxylic acid derivatives where the first step is a nucleophilic acyl substitution and the second is a nucleophilic addition.
Negatively Charged Nucleophiles
Neutral Nucleophiles
Predict the product of the following nucleophilic acyl substitution reaction of benzoyl chloride with 2-propanol:
Strategy
A nucleophilic acyl substitution reaction involves the substitution of a nucleophile for a leaving group in a carboxylic acid derivative. Identify the leaving group (Cl – in the case of an acid chloride) and the nucleophile (an alcohol in this case), and replace one by the other. The product is isopropyl benzoate.
Solution
Which of the following compounds would be expected to be the most reactive towards nucleophilic acyl substitution? Briefly explain your answer.
a) b)
- Answer
-
a) Compound A would be expected to be the more reactive. For two compounds with the same carboxylic acid derivative group, the one with the least steric crowding on the acyl side is typically the most reactive.
b) Compound B would be expected to be the more reactive. In general, acid anhydrides are more reactive than esters.
- Answer
-
-
The nucleophile is negatively charged, it will use the pair of electrons to make the attack, and the leaving group will leave with the negative charge, leaving the final molecule neutral.
-
The nucleophile is neutral, it uses the non-bonded pair of electrons to make the initial attack. Then, the leaving group will leave with the negative charge, for the final molecule to be neutral, a proton needs to be removed.
-
d. e.
f. CH 3 CO 2 – Na + g. CH 3 CONH 2 h. CH 3 CO 2 CH 3 + CH 3 CO 2 – Na + i. CH 3 CONHCH 3
-
The following structure represents a tetrahedral alkoxide ion intermediate formed by addition of a nucleophile to a carboxylic acid derivative. Identify the nucleophile, the leaving group, the starting acid derivative, and the ultimate product.
- Answer
-


4.4: The Complex Plane
A convenient way to conceptualize a complex number is to think of it as a point on a two-dimensional plane, called the complex plane , as shown in the figure below. The real and imaginary parts are the horizontal and vertical Cartesian coordinates in the plane. The horizontal ( \(x\) ) and vertical ( \(y\) ) coordinate axes are called the “real axis” and the “imaginary axis”, respectively.
Polar representation
If we think of a complex number as a point on the complex plane, its position can also be represented using polar coordinates instead of Cartesian coordinates. For a complex number \(z = x + i y\) , we can introduce polar coordinates \(r\) and \(\theta\) (both real numbers), such that \[r = \sqrt{x^2 + y^2}, \;\;\; \theta = \tan^{-1}(y/x).\] Conversely, \[x = r\cos\theta, \;\;\; y = r\sin\theta.\] These are the usual formulas for performing a change of coordinate between two-dimensional Cartesian coordinates and polar coordinates, as shown below. The radial coordinate is the magnitude of the complex number: \(r = |z|\) . The azimuthal coordinate \(\theta\) is called the argument of the complex number, which is also denoted by \(\mathrm{arg}(z)\) .
Note, by the way, that the complex zero, \(z = 0\) , has zero magnitude and undefined argument.
Using Euler’s formula (4.3.1), we can write \[\begin{align} z &= r\cos(\theta) + i r\sin(\theta)\\ &= r \left[\cos(\theta) + i \sin(\theta)\right] \\ &= r \, e^{i\theta}.\end{align}\] Therefore, whenever we can manipulate a complex number into a form \(A e^{iB}\) , where \(A\) and \(B\) are real numbers, then \(A\) is the magnitude and \(B\) is the argument. This is used in the following example:
Example \(\PageIndex{1}\)
For \(z \in \mathbb{C}\) , it can be shown that the magnitude and argument of \(\exp(z)\) are: \[\left|\exp(z)\right| = e^{\mathrm{Re}(z)}, \quad \mathrm{arg}\left[\exp(z)\right] = \mathrm{Im}(z).\] Proof: Let \(z = x + i y\) , where \(x, y \in \mathbb{R}\) ; then \[e^{z} = e^{x + i y} = e^x \, e^{iy}.\] By inspection, the magnitude of this complex number is \(e^x\) , and its argument is \(y\) .
Geometrical interpretation of complex operations
Using the complex plane, we can give useful geometric interpretations to the basic operations on complex numbers:
-
Addition of two complex numbers can be interpreted as the addition of two coordinate vectors. If
\(z_1 = x_1 + i y_1\)
and
\(z_2 = x_2 + i y_2\)
, then \[z_1 + z_2 = \left(x_1 + x_2\right) + i\left(y_1 + y_2\right).\] Hence, the point corresponding to
\(z_1 + z_2\)
is obtained by adding the two coordinate vectors corresponding to
\(z_1\)
and
\(z_2\)
. From this, we can geometrically prove a useful inequality relation between complex numbers, called the “triangle inequality”: \[|z_1 + z_2| \le |z_1| + |z_2|.\]
-
Complex multiplication can be interpreted as a scaling together with a rotation. If
\(z_1 = r_1e^{i\theta_1}\)
and
\(z_2 = r_2e^{i\theta_2}\)
, then \[z_1 z_2 = \left(r_1 r_2\right) \,\exp[i(\theta_1 + \theta_2)].\] Hence, the point corresponding to
\(z_1 \, z_2\)
is obtained by scaling the
\(z_1\)
coordinate vector by a factor of
\(|z_2|\)
, and rotating it by an angle of
\(\theta_2\)
around the origin. In particular, multiplication by
\(e^{i\theta}\)
is equivalent to a rotation by angle
\(\theta\)
.
-
The conjugation operation (Section 4.2) is equivalent to reflection about the real axis. It moves a point from the upper half of the complex plane to the lower half, or vice versa.
Complex numbers have no ordering
One consequence of the fact that complex numbers reside in a two-dimensional plane is that inequality relations are undefined for complex numbers . This is one important difference between complex and real numbers.
Real numbers can be ordered , meaning that for any two real numbers \(a\) and \(b\) , one and only one of the following is true: \[a < b \;\; \mathrm{OR} \;\; a = b \;\; \mathrm{OR}\;\; a > b.\] In geometrical terms, these ordering relations exist because the real numbers reside along a one-dimensional line.
But since complex numbers lie in a two-dimensional plane, it is nonsensical to write something like \(z_1 < z_2\) , where \(z_1\) and \(z_2\) are complex numbers. (It is, however, valid to write \(|z_1| < |z_2|\) , since magnitudes are real.)


9.6: U.S. Department of Labor, Women's Bureau
-
-
Last updated
-
-
Save as PDF
-
The Women’s Bureau has outlined three major strategies to create more equity between sexes in the workforce:
-
Improve Workplace Practices and Supports:
The Women’s Bureau identifies, fosters, and promotes policies and efforts that enable women to succeed in their work and personal lives. Today’s labor force comprises an increasing number of working mothers and women who care for disabled or elderly family members. Many low-paying occupations that tend to employ large shares of women lack adequate flexibility, benefits, and supports.
-
Promote Greater Access to and Preparation for Better Jobs for Women:
The Women’s Bureau aims to help women prepare for, participate and advance in, and retain non-traditional, high-growth, and higher-paying jobs. Female-dominated occupations have been found to pay less than male-dominated occupations with the same skill levels, and women have relatively low shares of employment in high-paying jobs such as those in transportation, construction, and science, technology, engineering, and math (STEM) fields.
-
Promote Fair Compensation and Equal Pay:
The Women’s Bureau seeks to educate workers on their rights and employers on their legal obligations to ensure fair compensation. Although women earn less than men for reasons such as the lower-paying jobs they traditionally perform, around 40% of the difference in wages remains unexplained. The Bureau conducts research to identify additional factors that contribute to the wage gap and how to overcome them, as well as look for ways to improve compensation for lower-wage jobs that employ large numbers of women.300
300
U.S. Department of Labor, Women’s Bureau. Updated 2016.
https://www.dol.gov/wb/overview_14.htm
. Retrieved 10 October 2016.


2.2: Job Description
A great job description is your road map to successful hiring, training, and evaluation. A job description summarizes the duties, responsibilities, and qualifications required for the position. A clear job will not only make every step of the hiring process easier, it will also make other human resources functions easier and more streamlined. (See Appendix 1 for an example of a job description.)
Here are some guidelines for creating an effective job description.
-
Identify the main duties and responsibilities of the position.
- Summarize the most critical or important functions.
- List the daily, weekly, monthly, and annual tasks or responsibilities of the position. Use descriptive verbs to identify the skills required (e.g., manage serving staff, resolve customer complaints, coordinate shift schedules, complete food orders).
-
Be specific about the qualifications, skills, and experience required.
- Consider requirements for education, work experience, technical skills, and “soft” skills (i.e., interpersonal skills, attitude) that an employee must have to succeed in the position.
- Identify the specific skills that you require (e.g., ability to solve problems with staff and guests tactfully and efficiently).
- Specify to what degree the candidate needs to possess the skills you require (e.g., for keyboarding skills, specify the speed and accuracy expected).
- Include the level of education and training needed to meet the requirements of the job.
- Be sure to include any specific training prerequisites (e.g., Red Seal, WorldHost, FOODSAFE, Serving It Right certificates), as well the number of years of experience in a similar position (e.g., minimum two years’ experience working in a high-volume restaurant).
- Determine which skills are essential for the position and which are an asset but not absolutely necessary.
- Be clear to what degree you are willing to train successful candidates once they are hired (such as offering an apprenticeship).
- Be realistic. Asking for too much may prevent suitable applicants from applying; asking for too little may attract too many underqualified applicants.
- Identify to which position this position reports.
- List which positions report to this position. In both these cases, the people in the positions may change but the reporting structure would not necessarily change.
-
Date the document.
- Job descriptions are not static documents. As positions within the organization and the needs of the organization change, so do the job requirements. Therefore the job description needs to reflect these changes, and knowing the date the job description was last reviewed is very helpful.
In short, be sure to include the following components when creating a job description:
- Job title
- Main duties and responsibilities
- Skills, qualifications, and experience required
- Equipment and tools required
- Training requirements
- Working conditions (e.g., any travel requirements, heavy lifting expectations, hours of work, whether inside or outside work)
- Reporting structure
- Date


2.10: S11. The Friedmann Equation - SOLUTIONS
Exercise 11.1.1
- Answer
-
K.E. is \(\frac{1}{2}mv^2\), where \(v = \dot a \ell\), so the test particle's kinetic energy is
\[\begin{equation*}
\begin{aligned}
\frac{1}{2}m\dot a^2 \ell ^2
\end{aligned}
\end{equation*}\]
Exercise 11.1.2
- Answer
-
P.E. is \(-\frac{GM(<d)m}{d}\), where by \(M(<d)\) we mean the mass contained in the sphere of radius \(d\), so \(M(<d) = \frac{4}{3}\pi d^3 \rho.\)
Therefore the test particle's potential energy is
\[\begin{equation*}
\begin{aligned}
-G \frac{4}{3} \pi \rho d^2 m
\end{aligned}
\end{equation*}\]
Exercise 11.1.3
- Answer
-
\[\begin{equation*}
\begin{aligned}
\frac{1}{2}m\dot a^2 \ell ^2 - G \frac{4}{3} \pi \rho d^2 m = \kappa
\end{aligned}
\end{equation*}\]
Exercise 11.1.4
- Answer
-
Recall that \(d = a \ell \; \Longrightarrow \; \ell = \frac{d}{a}\), substituting this in and rearranging our equation we get
\[\begin{equation*}
\begin{aligned}
\frac{1}{2}md^2 \frac{\dot a^2}{a^2} - \frac{1}{2}md^2 \frac{8\pi G\rho}{3} = \kappa
\end{aligned}
\end{equation*}\]dividing through by \(\frac{1}{2}md^2\) gives
\[\begin{equation*}
\begin{aligned}
\frac{\dot a^2}{a^2} - \frac{8\pi G\rho}{3} = \frac{2\kappa}{m}\frac{1}{d^2}
\end{aligned}
\end{equation*}\]Then we substitute back in \(d = a \ell\) and solve for \(\big(\frac{\dot a}{a}\big)^2\):
\[\begin{equation*}
\begin{aligned}
\left(\frac{\dot a}{a}\right)^2 = \frac{8\pi G \rho}{3} + \frac{2\kappa}{ml^2} \times \frac{1}{a^2}
\end{aligned}
\end{equation*}\]


2.1: Introduction
-
- Last updated
- Save as PDF
- Ly-Huong T. Pham, Tejal Desai-Naik, Laurie Hammond, & Wael Abdeljabbar
- ASCCC Open Educational Resources Initiative (OERI)
Information systems are made up of six components: hardware, software, data, communication, people, and process. In this chapter, we will review hardware. Hardware is the tangible or physical parts of computing devices to function. We will review the components of information systems, learn how it works, and discuss some of the current trends.
As stated above, computer hardware encompasses digital devices that you can physically touch. This includes devices such as the following:
- desktop computers
- laptop computers
- mobile phones
- smartphones
- smartwatches
- tablet computers
- e-readers
- storage devices, such as flash drives
- input devices, such as keyboards, mice, and scanners
- output devices such as 3d printers and speakers
Besides these more traditional computer hardware devices, many items that were once not considered digital devices are now becoming computerized. Digital technologies are now being integrated into many everyday objects, so the days of a device being labeled categorically as computer hardware may be ending. Examples of these types of digital devices include automobiles , refrigerators , and even soft-drink dispensers . In this chapter, we will also explore digital devices, beginning with defining the term .
Digital Devices
A digital device is any equipment containing a computer or microcontroller; included in these devices are smartphones, watches, and tablets. A digital device processes electronic signals that represent either a one (“on”) or a zero (“off”). The presence of an electronic signal represents the “ on ” state ; the absence of an electronic signal represents the “ off ” state . Each one or zero is referred to as a bit (a contraction of binary digit); a group of eight bits is a byte. The first personal computers could process 8 bits of data at once; modern PCs can now process 128 bits of data at a time. The larger the bit , the faster information can be processed simultaneously.
Sidebar: Understanding Binary
As you know, the system of numbering we are most familiar with is base-ten numbering. In base-ten numbering, each column in the number represents a power of ten, with the far-right column representing 10^0 (ones), the next column from the right representing 10^1 (tens), then 10^2 (hundreds), then 10^3 (thousands), etc. For example, the number 1010 in decimal represents: (1 x 1000) + (0 x 100) + (1 x 10) + (0 x 1).
Computers use the base-two numbering system, also known as binary. In this system, each column in the number represents a power of two, with the far-right column representing 2^0 (ones), the next column from the right representing 2^1 (tens), then 2^2 (fours), then 2^3 (eights), etc. For example, the number 1010 in binary represents (1 x 8 ) + (0 x 4) + (1 x 2) + (0 x 1). In base ten, this evaluates to 10.
As digital devices' capacities grew, new terms were developed to identify the capacities of processors, memory, and disk storage space. Prefixes were applied to the word byte to represent different orders of magnitude. Since these are digital specifications, the prefixes were originally meant to represent multiples of 1024 (which is 210) but have more recently been rounded to mean multiples of 1000.
The following table contains a listing of Binary prefixes:
|
Prefix |
Represents |
Example |
|---|---|---|
|
kilo |
one thousand |
kilobyte=one thousand bytes |
|
mega |
one million |
megabyte=one million bytes |
|
Giga |
one billion |
gigabyte=one billion bytes |
|
tera |
one trillion |
terabyte=one trillion bytes |
|
Peta |
one quadrillion |
petabyte=one quadrillion bytes |
|
exa |
one quintillion |
exabyte=one quintillion bytes |
|
Zetta |
one sextillion |
zettabytes=one sextillion bytes |
|
yotta |
one septillion |
yottabytes=one septillion bytes |


4.4: What are the benefits and drawbacks of home schooling?
-
- Last updated
- Save as PDF
By: Megan Galligan
Introduction
Many believe that home schooling has its roots in the 1960s though the 1970s when educational reform became an issue on the national forefront (Dobson, 2000, paragraph 5). Actually, until 1852, public school attendance was not mandatory. It was only in 1852 that the state of Massachusetts made the first compulsory attendance law and eventually all other states followed suit. (All About Parenting). Parents are faced with the option to send their children to public or private schools, or to keep their children at home to educate the children themselves. The parents must consider many aspects of education to make this decision including their educational aptitude as teachers, the possible social effect on the children, the production of good citizens, the attention the children need to learn, and the external pressures of the school systems placed on the children.
Currently 3%-4% of the US school-going population is homeschooled. 51% of homeschooled students are female while 49% are male. White students make up the bulk of homeschooled students at 68%. Hispanics make up about 15%; Black students account for 8%; Asian students make up about 4%. Until 2019, the number of homeschooled students had been growing by 2% to 8% each year. From 2019 to the fall of 2020, the percentage of homeschooled students changed from 3.4% to 9%.
Pros of Home Schooling
Home schooled children had many more freedoms than other children in public school settings. They have Educational freedom giving them choices to learn what they want with subjects that interest them. They have physical freedom to have more hands on experiences such as field trips to museums or aquariums. Religious freedoms is one of the largest gains of home schooling for most families. They have the opportunity to incorporate their religious and spiritual beliefs without standards and rules to abide by. According to the Journal of College Admissions , home schooling is the fastest growing forms of educating children (Ray, 2004, paragraph 2). It is estimated that there are 1.7 to 2.1 million students in grades k-12 that are enrolled in home school as of 2003 and that number seems to be growing every year (Ray, 2004, paragraph 2). Home schooling began as a way for parents to have more control over the curriculum being taught to their children (Cooper and Sureau, 2007, paragraph 9). There were two major view points considered when deciding to remove a child from public school and continuing the education at home. Parents either believed that public schooling developed topics that conflicted with the religious teachings or believed that they, as parents, could serve as a better educator for their children (Cooper and Sureau, 2007, paragraph 9).
In an article written by Michael Romanowski, a professor at Ohio Northern University, he states that “No other factor in life will have more of an effect on a child's life than the family, and home schooling enables the family to play its important role more actively”(2001, paragraph 6). Home schooling also allows the parents more of and opportunity to become involved in all aspects of the child’s life because they become the focal point in all aspects of their life. In Romanowski’s article, he also states that the intensified relationship with the parents will extend to other siblings that are also being home schooled. He believes that the since of communication is strengthened which allows a more personal relationship (2001, paragraph 7).
There is also the argument that home schooled individuals grow up to become more well rounded citizens. According to a separate article by Romanowski, 71 percent of people who were home schooled were involved in community service(2007, paragraph 14). Moreover, only 37 percent of individuals who were educated in the public school system were involved in public service activities (Romanowski, 2007, paragraph 14). The percentage variations also exist when examining topics such as young voters aged eighteen to twenty-four, contributions to a political party, and active participation in local politics (Romanowski, 2007, paragraphs 15,16,17, and 18)
Another reason for parents choosing the option of home schooling is for the protection of their children. It seems that reports of violence in schools in the news and media are increasing. For example, weapons being brought into public and private schools; increase in gangs; bulling and fights have become more violent; and acts against students are being video taped and broadcast on the internet. These are a few of the reasons why some parents feel that public as well as private schools are no longer safe. Although news reports of such violence seems to be increasing, the percentage of violent acts occurring in public schools has decreased; yet students’ absence due to fear of violence has increased. According to the National Indictors for Education Statistics, “There is some evidence that student safety has improved. The victimization rate of students ages 12–18 at school declined between 1992 and 2005. However, violence, theft, drugs, and weapons continue to pose problems in schools” (“Indicators of School Crime and Safety,” 2007). Furthermore, some parents who home school do so as a way of protecting their children from the exposure to drugs, alcohol, tobacco, and premarital sex. Parents who home school are able to teach their children about these issues in a way that supports their beliefs. By home schooling their children they believe that they can provide them with a well rounded education in the safety of their own home.
Public education uses a set curriculum to teach all children in a given classroom. The classroom is filled with a variety of learning styles, interests, and abilities. For the parent who has chosen to educate their child at home, the curriculum can be catered to meet each child's individual needs, interests and learning style. There is also the element of time. More personalized time is given to the child at home and there is not the waisted time standing in line for lunch, recess, others to finish their work, etc. and therefor much of the schoolwork is completed much earlier in the day, leaving time for real life learning experiences. (All About Parenting).
I have also discerned that parents who are teaching their children at home also have the benefit of the one-on-one interaction with the child. The child does not need to pace them self with the other members of the classroom. They have the freedom to spend extra time on a troubling topic or to speed through a trivial part of a subject.
Note
Amos Bronson Alcott, a teacher and writer from the 19th century once said, "A true teacher defends his pupils against his own personal influence". Is this possible when it is a parent teaching their child?
Cons of Home Schooling
On the other side of the issue there are many downsides of homes schooling that need to be accounted for. Parents who home school their children struggle with time constraints for getting all of the work load done by one person. This can consist of creating a schedule, activities, learning, and hands on projects/trips. Aside from time restraints there are many financial restraints as well, having one parent in the working world and one in the teaching world can cause some financial strain. In the article “The Pros and Cons of Homeschooling” Isabel Shaw says, “Surprisingly, most home schooling families believe that the brief loss of income is well worth the satisfaction of watching their kids grow and learn in freedom.” In an article by Susan Orloff, she states that there are certain things learned in the school setting that do not occur in other environments but they “…in the school setting they are happening every day” (Orloff, 2005, paragraph 5). These things include making friends, learning to follow directions, and becoming able to handle deadlines. Orloff also states that she has “All too often… seem home schooling as an escape from school and pressures that structured environment demands” (Orloff, 2005, paragraph 7). However, note that many home schoolers participate in peer groups that allow for some of these things to happen.
Another factor that should be considered in the choice to home school is that added financial burden. Families spend an average of $400 per child each year to cover costs of curriculum, softwar, field trips, materials for projects, etc. (All About Parenting)
If the reason behind taking the child out of public school and beginning home school is to decrease the pressures that the public school produces, it could only lead to the future detriment of the child. The child needs to be able to develop coping skills to deal with the trials that life would present. Set backs allow a person to grow and develop the skills to combat similar situations in the future. Taking the child out of public education for this reason only teaches the child to escape their problems, not how to learn from them.
Based on the data provided by the Home School Legal Defense Team, 92% of who parents make the decision to home school their children intend to have the child’s entire education at home, grades K-12 (Ray, 1997). Although the majority intend to complete they education at home, only 26% of students can claim to have over ten years of their schooling at home (Ray, 1997). These statistics seem to imply some type of inconsistence in schooling. On average, of high school graduates who were home schooled can claim 6.9 years of home schooling (Ray, 1997). This seems to require quite an adjustment for the children in school. They are required to go in between home and public school and make the required modifications socially and academically.
In Romanowski’s article, “The Strengths and Limitations of Home Schooling”, he states that “To receive a complete education, students need to engage in discussions, share ideas, compete, and work with other students” (2001, paragraph 19). He believes that in order to strengthen the ideas, a person must get feedback and criticism on those ideas. The original idea seems to change, expand, and grow with the input of others. He also introduces the idea that the parent that becomes the primary educator might not have the proper background to adequately teach the upper level subject to the children (Romanowski, 2001, paragraph 24). He questions whether parents have the ability to teach their children “…higher levels of math, complex biological terms, or an in dept analysis of American history” (Romanowski, 2001, paragraph 24). A parent may be knowledgeable in some of the subjects required, but it would be astonishing if they were skilled enough to teach in all areas.
Home Schooling and the Federal Government
Once an isolated practice with little support, home schooling “has now reached a level of unprecedented visibility, politicization, and publicization” (Cooper, p. 111). Parents and advocates have gained significant legal, political, and social ground, substantially raising public awareness. Subsequently, the increase in home schooling’s power and popularity has caused state and local educational leaders to adjust some of their policies. This has brought considerable criticism from supporters of the “democratic, public control of education” (Cooper, pg 112). They claim home schooling “denies democratic accountability” (Cooper, pg. 112) and is “detrimental to the common good” (Cooper, pg. 115).
Note
Despite political pressure to conform, homeschool families have become well informed, active, and influential - all qualities that are critical to the public life of society (Cooper, pg. 132).
In light of this fiery opposition, how far legally and constitutionally can the federal government go to regulate home schooling and overturn parents’ rights? Twenty years ago, home schooling was considered a crime, and although many states began legalization in 1999, the court controversies are far from over. The cases range in variety and often address attendance, parent qualifications, supervision, and dual-enrolment in public facilities (Cooper, pg. 123).
In most recent legislation, the Second District Court of Appeals in Los Angeles, CA stated in February 2008 that “children ages six to 18 may be taught only by credentialed teachers in public or private schools — or at home by Mom and Dad, but only if they have a teaching degree” (Kloberdanz-Modesto). California’s governor, Arnold Schwarzenegger, defended parents’ rights for the well-being of their child and guaranteed protest (Kloberdanz-Modesto). This decision is merely another pull by the federal government in the tug-of-war being played with home school advocates.
Conclusion
There seem to be many considerations before deciding which type of schooling is best for a child. What seems to be the overriding factor is that all children are different. It depends of the individual when deciding if home school is a plausible option. There seems to be pros and cons that balance each other. The benefits and the detriments are comparable. The education of children seems to be an extremely important and personal decision that all parents face. Yet, will this decision stay in the parents' hands? The constant influx of court cases addressing the uses and abuses of homeschooling makes the future of home schooling unpredictable.
Works Cited
Cooper, b. and Sureau, J. (2007). The politics of home schooling: new developments, new challenges. Educational policy, 21 no10, 111-132. Retrieved April 16, 2008 from SAGE Publications.
Kloberdanz-Modesto, K. (2008). Criminalizing home schoolers. TIME Magazine. Retrieved April 16, 2008, from www.time.com/time/nation/article/0,8599,1720697,00.html.
Orloff, S. (2005). Facts to Consider before Home Schooling. The Exceptional Parent, 39 no4 54. Retrieved February 3, 2008 from ODU Library Database.
Romandowski, M. (2001). Common Arguments about the Strengths and Limitations of Home Schooling. The Clearing House, 72 no 2 79-83. Retrieved February 3, 2008, from ODU Library Database.
Romandowski, M. (2006). Revisiting the Common Myths about Home Schooling. The Clearing House, 79 no3 125-9. Retrieved February 3, 2008, from ODU Library Database.
Ray, B. (2004). Home Schoolers on to College: What Research Shows Us. Journal of College Administration, no.185 5-11. Retrieved February 3, 2008, from ODU Library Database.
Ray, B. (1997). How Long Are They Going to Home School?: Fig 17.1 Parents’ Intent to Continue Home School Education. Home School Legal Defense Association. Retrieved February 3, 2008 from www.hslda.org/docs/study/ray1997/21.asp.
Ray, B. (1997). How Many Years Were Home School Graduates Taught at Home?: Fig.18.0. Home School Legal Defense Association. Retrieved February 3, 2008 from www.hslda.org/docs/study/ray1997/22.asp.
Shaw, Isabel, (2008). The Pros an Cons of Homeschooling. retrieved April 18, 2008 from school.familyeducation.com/home-schooling/parenting.
National Center for Education Statistics, Institute of Education Sciences, US Department of Education. Indicators of School Crime and Safety: 2007. nces.ed.gov/programs/crimeindicators/crimeindicators2007/index.asp
"Advantages and Disadvantages of Home schooling." Retrieved April 26, 2008. www.allaboutparenting.org


Check the methods of communication you would most likely use for each of the following.  Do you find that there were definitely different purposes to how and why you used email instead of the phone, or Snapchat instead of a letter? It is good for you to reflect on your communication choices so that they are always most effective.
Look at the forms of communication you chose for “boss.” Perhaps you chose face-to-face and email as the two forms of communication you would use with your boss. Think through how those might have had an effect on the success of your communication with them. Now select two other forms of communication. Would you have been able to get the same response from your boss?


6.5: Non-Salary Negotiable Items
Other things to negotiate in a job offer
Negotiating an employment contract is an important part of obtaining a new job. However, there are items you can negotiate aside from your base salary. Learning what types of non-salary items are negotiable can help you understand what to ask for during the negotiation process. In this article, we list 18 non-salary negotiable items that you can address with your new employer and discuss the benefits of negotiating for these items.
Benefits of negotiating for non-salary items
Non-salary items such as company benefits, subsidies or office amenities can dramatically improve your work experience. Some items, such as commissions or stock options, may even give you the opportunity to earn more money. Negotiating non-salary items also allows you to practice your negotiating skills on items that employers may be more willing to negotiate about.
18 common non-salary negotiable items
Here are a few items that you can negotiate outside of your base salary:
1. Start date
If a company offers you a start date that's earlier or later than you'd like, you can negotiate about when to begin the position. This can be useful if you're relocating, have prior commitments such as a vacation, need to finish your previous employment or need more time to prepare for your transition. Let your employer know about any reasons you may need to adjust your start date to determine if they're open to negotiation.
2. Job title
Sometimes you may find your given job title insufficient or inaccurate. Your employer may change your title slightly to an offered alternative that more accurately describes your duties. Before a negotiation, consider listing reasons your title should change and possible new title options.
3. Commission percentage
If you work in a sales role, you may earn commission based on your sales rate. You can negotiate a higher commission percentage so that you earn more from the sales you produce. For example, if you earn the company $10,000 in toaster sales per quarter and your commission percentage is 10%, your employer adds $1,00 to your next paycheck. If you negotiate your commissions to 15%, then your $10,000 dollars in toaster sales can earn you $500 more that quarter.
4. Travel benefits
If your job requires you to travel often, you can negotiate to keep your travel rewards points. Keeping travel rewards points, such as frequent flier miles or hotel loyalty programs, can save you money when you travel on your own for vacations or to visit family. You may also try to negotiate for better travel benefits while traveling for your work, such as upgraded flight classes or higher quality hotels.
5. Moving expenses
When a job requires you to relocate, the company may provide assistance or reimbursement for your moving expenses. While they may not cover all of your travel costs, negotiating for moving benefits can help you afford relocation and may increase your chances of accepting a position far from your current home. If you've accepted a distant position, consider including moving reimbursement in your negotiations.
6. Transportation benefits
Employers can offer reimbursements or travel credits to help cover the costs of traveling to work. Depending on where you live and how you commute, companies may provide gas subsidies, bus fare or free parking spaces. Ask your employer while negotiating about potential transportation benefits.
7. Retirement benefits matching
Many organizations offer the option to open a matching retirement plan in which the company matches any money you place into the account. The matching rate can vary depending on the company and type of retirement plan. You can negotiate for better matching rates or additional retirement benefits.
8. Phone allowance
If your job requires you to talk for long periods of time on your own phone, you can negotiate for your company to subsidize part of your phone plan as a work expense. Some organizations may even provide you a work phone with a fully paid phone plan. Ask your employer if they're willing to cover some of your phone expenses during the negotiation process.
9. Discounts on company products
Certain companies may offer the opportunity to buy or use their products or services at a discounted rate. For example, if you work at Yippee Cellular as a sales representative (opens in new window) , you may get a 30% discount on your cell phone plan. You can negotiate the amount of these discounts and whether they apply to you as an individual or your entire family.
10. Signing bonus
A signing bonus is an amount of extra money that an employer gives you when you sign an employment contract for a new position. A signing bonus can help you relocate or cover any other costs of switching jobs. Consider negotiating for a signing bonus, especially when you can't negotiate for a higher salary.
11. Remote work
As technology improves, many organizations are allowing people to work some days remotely or perform all of their main duties at home. Limiting your days at the office can give you the freedom to work in a more comfortable environment or live far away from your company's building without worrying about a long commute. If you work in a position that you can perform at home, consider negotiating for more remote workdays.
12. Equity compensation
Equity compensation is a noncash investment option that represents employee ownership of the company. It may include stock, performance shares and options. Startups often offer equity options to employees to help compensate for any company risk. If you're working for a startup or other small company, consider negotiating for some of the company's equity.
13. Guaranteed severance package
A severance package is a collection of benefits that you can receive if your company fires you. Asking a company to guarantee you a severance package can help protect you if something unexpected happens within the organization. It may also encourage them not to fire you if you've negotiated a large severance package.
14. Office space
A quality work area can help you organize and may increase your productivity. When negotiating for a job, you can ask about your working arrangements. You can try to negotiate for an office instead of a cubicle, a larger office or an office with a better view.
15. Tuition reimbursement
Companies sometimes offer tuition reimbursement or loan forgiveness programs for employees who choose continuing education. They usually require you to work for them for a certain period of time before helping with education costs. Try to negotiate for a higher reimbursement rate or a shorter required time before reimbursement.
16. Daycare reimbursement
Quality childcare for your children during working hours is often expensive. Companies may offer subsidies or reimbursement for childcare costs while you're working. Some organizations may also have their own daycare providers. Consider mentioning childcare when negotiating with an employer to hear about their programs and potential subsidies.
17. Flexible scheduling
Depending on your job duties, your organization may allow you to set your own work hours or add flexibility to your scheduling. A flexible schedule can empower you to work during your best hours of focus or may allow you to work around life obligations, such as doctor's appointments. Talk to your supervisor about ways you can negotiate for a schedule that meets your needs.
18. Additional leave
You can negotiate for extra days off to use for vacation, volunteering or sick days. Some companies may also allow you to negotiate when you can start using your leave. For example, if your company usually lets employees use their vacation time after 90 days, you can negotiate to use yours after 60 days.
Source: "18 Non-Salary Negotiable Items To Consider for Your New Job" , Indeed Editorial Team, June 28, 2024.


4.1: Independence of Events
Historically, the notion of independence has played a prominent role in probability. If events form an independent class, much less information is required to determine probabilities of Boolean combinations and calculations are correspondingly easier. In this unit, we give a precise formulation of the concept of independence in the probability sense. As in the case of all concepts which attempt to incorporate intuitive notions, the consequences must be evaluated for evidence that these ideas have been captured successfully.
Independence as lack of conditioning
There are many situations in which we have an “operational independence.”
- Supose a deck of playing cards is shuffled and a card is selected at random then replaced with reshuffling. A second card picked on a repeated try should not be affected by the first choice.
- If customers come into a well stocked shop at different times, each unaware of the choice made by the others, the the item purchased by one should not be affected by the choice made by the other.
- If two students are taking exams in different courses, the grade one makes should not affect the grade made by the other.
The list of examples could be extended indefinitely. In each case, we should expect to model the events as independent in some way. How should we incorporate the concept in our developing model of probability?
We take our clue from the examples above. Pairs of events are considered. The “operational independence” described indicates that knowledge that one of the events has occured does not affect the likelihood that the other will occur. For a pair of events {\(A\), \(B\)}, this is the condition
\(P(A|B) = P(A)\)
Occurrence of the event \(A\) is not “conditioned by” occurrence of the event \(B\). Our basic interpretation is that \(P(A)\) indicates of the likelihood of the occurrence of event \(A\). The development of conditional probability in the module Conditional Probability , leads to the interpretation of \(P(A|B)\) as the likelihood that \(A\) will occur on a trial, given knowledge that \(B\) as occurred. If such knowledge of the occurrence of \(B\) does not affect the likelihood of the occurrence of \(A\), we should be inclined to think of the events \(A\) and \(B\) as being independent in a probability sense.
Independent pairs
We take our clue from the condition \(P(A|B) = P(A)\). Property (CP4) for conditional probability (in the case of equality) yields sixteen equivalent conditions as follows.
| \(P(A|B) = P(A)\) | \(P(B|A) = P(B)\) | \(P(AB) = P(A) P(B)\) |
| \(P(A|B^c) = P(A)\) | \(P(B^c|A) = P(B^c)\) | \(P(AB^c) = P(A) P(B^c)\) |
| \(P(A^c|B) = P(A^c)\) | \(P(B|A^c) = P(B)\) | \(P(A^c B) = P(A^c)P(B)\) |
| \(P(A^c|B^c) = P(A^c)\) | \(P(B^c|A^c) = P(B^c)\) | \(P(A^cB^c) = P(A^c) P(B^c)\) |
| \(P(A|B) = P(A|B^c)\) | \(P(A^c|B) = P(A^c|B^c)\) | \(P(B|A) = P(B|A^c)\) | \(P(B^c|A) = P(B^c|A^c)\) |
These conditions are equivalent in the sense that if any one holds, then all hold. We may chose any one of these as the defining condition and consider the others as equivalents for the defining condition. Because of its simplicity and symmetry with respect to the two events, we adopt the product rule in the upper right hand corner of the table.
Definition. The pair {\(A\), \(B\)} of events is said to be (stochastically) independent iff the following product rule holds:
\(P(AB) = P(A) P(B)\)
Remark . Although the product rule is adopted as the basis for definition, in many applications the assumptions leading to independence may be formulated more naturally in terms of one or another of the equivalent expressions. We are free to do this, for the effect of assuming any one condition is to assume them all.
The equivalences in the right-hand column of the upper portion of the table may be expressed as a replacement rule , which we augment and extend below:
If the pair {\(A\), \(B\)} independent, so is any pair obtained by taking the complement of either or both of the events.
We note two relevant facts
- Suppose event \(N\) has probability zero (is a null event). Then for any event \(A\), we have \(0 \le P(AN) \le P(N) = 0 = P(A)P(N)\), so that the product rule holds. Thus {\(N\), \(A\)} is an independent pair for any event \(A\).
- If event \(S\) has probability one (is an almost sure event), then its complement \(S^c\) is a null event. By the replacement rule and the fact just established, \({S^c\), \(A\)} is independent, so {\(S\), \(A\)} is independent.
The replacement rule may thus be extended to:
If the pair {\(A\), \(B\)} independent, so is any pair obtained by replacing either or both of the events by their complements or by a null event or by an almost sure event.
- Unless at least one of the events has probability one or zero, a pair cannot be both independent and mutually exclusive. Intuitively, if the pair is mutually exclusive, then the occurrence of one requires that the other does not occur. Formally: Suppose \(0 < P(A) < 1\) and \(0 < P(B) < 1\). {\(A\), \(B\)} mutually exclusive implies \(P(AB) = P(\emptyset) = 0 \ne P(A) P(B)\). {\(A\), \(B\)} independent implies \(P(AB) = P(A) P(B) > 0 = P(\emptyset)\)
- Independence is not a property of events. Two non mutually exclusive events may be independent under one probability measure, but may not be independent for another. This can be seen by considering various probability distributions on a Venn diagram or minterm map.
Independent classes
Extension of the concept of independence to an arbitrary class of events utilizes the product rule.
Definition. A class of events is said to be (stochastically) independent iff the product rule holds for every finite subclass of two or more events in the class.
A class {\(A\), \(B\), \(C\)} is independent iff all four of the following product rules hold
\(P(AB) = P(A) P(B)\) \(P(AC) = P(A) P(C)\) \(P(BC) = P(B) P(C)\) \(P(ABC) = P(A) P(B) P(C)\)
If any one or more of these product expressions fail, the class is not independent. A similar situation holds for a class of four events: the product rule must hold for every pair, for every triple, and for the whole class. Note that we say “not independent” or “nonindependent” rather than dependent. The reason for this becomes clearer in dealing with independent random variables.
We consider some classical exmples of nonindependent classes
SOME NONINDEPENDENT CLASSES
-
Suppose {\(A_1\), \(A_2\), \(A_3\), \(A_4\)} is a partition, with each \(P(A_i) = 1/4\). Let
\(A = A_1 \bigvee A_2 B = A_1 \bigvee A_3 C = A_1 \bigvee A_4\)
Then the class {\(A\), \(B\), \(C\)} has \(P(A) = P(B) = P(C) = 1/2\) and is pairwise independent, but not independent, since \(P(AB) = P(A_1) = 1/4 = P(A) P(B)\) and similarly for the other pairs, but \(P(ABC) = P(A_1) = 1/4 \ne P(A)P(B)P(C)\) - Consider the class {\(A\), \(B\), \(C\), \(D\)} with \(AD = BD = \emptyset\), \(C = AB \bigvee D\), \(P(A) = P(B) = 1/4\), \(P(AB) = 1/64\), and \(P(D) = 15/64\). Use of a minterm maps shows these assignments are consistent. Elementary calculations show the product rule applies to the class {\(A\), \(B\), \(C\)} but no two of these three events forms an independent pair.
As noted above, the replacement rule holds for any pair of events. It is easy to show, although somewhat cumbersome to write out, that if the rule holds for any finite number \(k\) of events in an independent class, it holds for any \(k + 1\) of them. By the principle of mathematical induction, the rule must hold for any finite subclass. We may extend the replacement rule as follows.
If a class is independent, we may replace any of the sets by its complement, by a null event, or by an almost sure event, and the resulting class is also independent. Such replacements may be made for any number of the sets in the class. One immediate and important consequence is the following.
If {\(A_i: 1 \le i \le n\)} is an independent class and the the class {\(P(A_i):1 \le i \le n\)} of individual probabilities is known, then the probability of every minterm may be calculated.
Minterm probabilities for an independent class
Suppose the class {\(A\), \(B\), \(C\)} is independent with respective probabilities \(P(A) = 0.3\), \(P(B) = 0.6\), and \(P(C) = 0.5\). Then
{\(A^c\), \(B^c\), \(C^c\)} is independent and \(P(M_0） = P(A^c)P(B^c)P(C^c) = 0.14\)
{\(A^c\), \(B^c\), \(C\)} is independent and \(P(M_1) = P(A^c)P(B^c)P(C) = 0.14\)
Similarly, the probabilities of the other six minterms, in order, are 0.21, 0.21, 0.06, 0.06, 0.09, and 0.09. With these minterm probabilities, the probability of any Boolean combination of \(A\), \(B\), and \(C\) may be calculated
In general, eight appropriate probabilities must be specified to determine the minterm probabilities for a class of three events. In the independent case, three appropriate probabilities are sufficient.
Three probabilities yield the minterm probabilities
Suppose {\(A\), \(B\), \(C\)} is independent with \(P(A \cup BC) = 0.51\), \(P(AC^c) = 0.15\), and \(P(A) = 0.30\). Then \(P(C^c) = 0.15/0.3 = 0.5 = P(C)\) and
\(P(A) + P(A^c) P(B) P(C) = 0.51\) so that \(P(B) = \dfrac{0.51 - 0.30}{0.7 \times 0.5} = 0.6\)
With each of the basic probabilities determined, we may calculate the minterm probabilities, hence the probability of any Boolean combination of the events.
MATLAB and the product rule
Frequently we have a large enough independent class {\(E_1\), \(E_2\), \(\cdot \cdot\ cdot\), \(E_n\)} that it is desirable to use MATLAB (or some other computational aid) to calculate the probabilities of various “and” combinations (intersections) of the events or their complements. Suppose the independent class {\(E_1\), \(E_2\), \(\cdot \cdot\ cdot\), \(E_{10}\)} has respective probabilities
0.13 0.37 0.12 0.56 0.33 0.71 0.22 0.43 0.57 0.31
It is desired to calculate (a) \(P(E_1 E_2 E_3^c E_4 E_5^c E_6^c E_7)\), and (b) \(P(E_1^c E_2 E_3^c E_4 E_5^c E_6^c E_7 E_8 E_9^c E_{10})\).
We may use the MATLAB function prod and the scheme for indexing a matrix.
>> p = 0.01*[13 37 12 56 33 71 22 43 57 31]; >> q = 1-p; >> % First case >> e = [1 2 4 7]; % Uncomplemented positions >> f = [3 5 6]; % Complemented positions >> P = prod(p(e))*prod(q(f)) % p(e) probs of uncomplemented factors P = 0.0010 % q(f) probs of complemented factors >> % Case of uncomplemented in even positions; complemented in odd positions >> g = find(rem(1:10,2) == 0); % The even positions >> h = find(rem(1:10,2) ~= 0); % The odd positions >> P = prod(p(g))*prod(q(h)) P = 0.0034
In the unit on MATLAB and Independent Classes, we extend the use of MATLAB in the calculations for such classes.


15.12B: Hydatid Disease
- Outline the life cycle of Echinococcus granulosus
Hydatid disease, commonly referred to as echinococcosis, is a result of infection by the tapeworm included in the Echinococcus spp. Echinococcus multilocularis results in alveolar echinococcosis and Echinococcus vogeli can cause polycystic echinococcosis. In individuals that develop alveolar echinococcosis, which is extremely rare, cysts develop and grow within the alveolar, liver, lungs, and brain. In the cases of alveolar echinococcosis, the parasite responsible, Echinococcus multilocularis, is associated with dogs, cats, wolves and most commonly, foxes, serving as the definitive hosts. The intermediate hosts include small rodents. In individuals that develop polycystic echinococcosis, there is the development of slow growing cysts within the body that exhibit the capability to infiltrate surrounding areas. Cysts are typically found in the liver and in the thorax or abdominal cavity. The parasite responsible for polycystic echinococcosis, Echinococcus vogeli , uses dogs or bush dogs as a definitive host and rodents as an intermediate hosts.
Echinococcus granulosus is a tapeworm found in dogs, who function as the definitive host, as well as sheep, cattle, goats, and pigs who serve as intermediate hosts. Echinococcus granulosus are capable of infecting humans, resulting in hydatid disease, and cause slowly enlarging cysts that develop in vital organs such as the liver or lungs, also referred to as cystic echinococcosis. However, the growth of these cysts are slow and may go unnoticed for a significant duration of time. This form of echinococcosis is more prevalent and commonly found in humans. The adult Echinococcus granulosus targets the small bowel of the definitive hosts and release eggs through the feces. After ingestion by the intermediate hosts, the eggs will hatch and penetrate the intestinal wall. The exiting of the intestinal wall results in circulation of oncospheres that will target various organs, including the liver and lungs. The oncospheres undergo further growth and form cysts. The definitive host will then become infected upon ingestion of the cyst-containing organs of the infected intermediate host. It is within the definitive host that the cyst will develop into the adult stage and the cycle continues and repeats.
Hydatid disease is characterized by the growth of these cysts into the adult stage for the tapeworm. Individuals infected with Echinococcus species that develop hydatid disease may not develop symptoms for many years after infection. However, if symptoms develop, it may present in the form of pain or discomfort due to the growing cysts in the upper abdominal regions. Additionally, rupture of fluid within the cysts can result in various medical issues including allergic reactions or death.
Key Points
- Echinococcus granulosus causes hydatid disease, or cystic echinococcus and causes slowly enlarging cysts to develop in vital organs.
- Echinococcus multilocularis results in alveolar echinococcosis and Echinococcus vogeli can cause polycystic echinococcosis.
- Individuals infected with Echinococcus species who develop hydatid disease may not develop symptoms for many years after infection.
Key Terms
- echinococcosis : a parasitic disease of both animals and humans, also known as hydatid disease.


7.10: Planet Mars
Mars is the fourth planet from the Sun. It is historically called the Red Planet because of its reddish appearance in Earth’s night sky. Mars has some Earth-type characteristics, such as Polar Caps, clouds, and water in at least the ice or solid phase. It was very active volcanically at one time. Numerous spacecraft have successfully explored Mars from orbit and the surface. It is by far the most-visited planet (by spacecraft) in our Solar System, besides Earth.
Differences between Martian North and South Polar Caps
North Polar Cap:
- Primarily composed of water ice, H2O
- Size of Greenland
- Seasonal
- Goes through a variety of change
South Polar Cap:
- Primarily composed of carbon dioxide ice, CO 2
- 1/10 the size of the North Polar Cap
- Always there
- On one side of Pole
The differences in the Martian polar caps are probably due to different polar climates. It’s important to note that Earth’s Polar Caps are also different; the North Pole is floating ice versus the South Pole as a continent.


1.1: Induction and Well-Ordering
In this section, we'll seek to answer the questions:
- What is the Well-Ordering Principle?
- What is mathematical induction, and how can we use it to prove statements about \(\mathbb{N}\)
In this section we will assume the basic algebraic/arithmetic properties of the integers such as closure under addition, subtraction, and multiplication, most of which we will formalize via axioms in subsequent sections. Axiom 1.1.1 : Well-Ordering Principle formalizes the familiar notion that nonempty subsets of the positive integers have a smallest element, which will be used repeatedly throughout the text. We then explore a closely related idea, mathematical induction, via an example and exercises.
The collection of natural numbers is denoted by \(\mathbb{N}\), and is the set,
\(\mathbb{N}=\{ 1 \text{,}2\text{,}3\text{,} \ldots \}\).
By \(\mathbb{N}_0\) we mean the set \(\mathbb{N} \cup {0}=\{ 0\text{,}1 \text{,}2\text{,}3\text{,} \ldots\}\).
In some sense, the fundamental properties of \(\mathbb{N}\) are (a) there is a smallest natural number, and (b) there is always a next natural numberIn fact, one can build a model of \(\mathbb{N}\) with set theory and the Peano axioms, which utilize the notion of a successor --the next natural number.). A consequence of the Peano postulates is the well-ordering principle , which we state as an axiom.
Every nonempty subset of \(\mathbb{N}_0\) contains a least (smallest) element under the usual ordering, \(\leq\).
- Note
-
Our word choice is suggestive. In fact, other orderings do exist, and while the set of no\(\mathbb{N}\)egative real numbers RR does not satisfy the well-ordering principle under the usual ordering \(\leq\), the Well Ordering Axiom asserts that there exists a well ordering on any set, including R.R. Accepting this axiom is equivalent to accepting the axiom of choice .
The Well-Ordering Principle is useful for producing smallest elements of nonempty subsets defined to have certain properties, as the following example demonstrates.
In this exploration, we investigate polynomials with real coefficients, as well as their degrees. We will define these terms more formally in Definition: Polynomial , but for now you may use your intuition from previous courses in algebra.
Let \(S\) be the set of all polynomials \(f\) in the variable \(x\) with real coefficients such that \(f(2)=f(−2)=0\) and \(f(0)=−4\).
- Give an example of an \(f\in S\) and \(g\notin S\).
- Let \(D=\{deg\; f : \; f\in S\}\) be the set of possible degrees of polynomials in \(S\). Show that \(D\neq \varnothing\) and \(D\subseteq \mathbb{N}_0\).
- Apply the Well-Ordering Principle to argue that \(D\) has a least element. To what does this correspond in \(S\)?
We will use this principle throughout the text, next in Theorem 1.2 .4 .
The set of integers consists of the positive and negative natural numbers, together with zero, and is denoted by \(\mathbb{Z}\):
\(\mathbb{Z}=\{ \ldots \; ,−3\; ,−2\; ,−1\; ,0\; ,1\; ,2\; ,3\; , \ldots \}\).
Let \(P(m)\) be a statement about the natural number \(m\) . Let \(k_0\in \ N\) be such that the statement \(P(k_0)\) is true (the base case ), and suppose there is an \(n\geq k_0\) such that for all \(k\) satisfying \(k_0 \leq k \leq n\), \(P(k)\) is true (the inductive hypothesis ). Then \(P(n+1)\) is true, and thus \(P(m)\) is true for all \(m\geq k_0\) (the inductive step ).
- Note
-
Sample statements could include “\(m\) is really interesting” or “\(3m^2+m+2\) is even”.
Mathematical induction is like climbing an infinite staircase. The base case tells us that we can take a first step on the staircase (\(k_0\)). In the inductive hypothesis , we assume we can take all the steps up to a certain height (\(\mathbb{N}\)). In the inductive step , we prove that this allows us to take the \((n+1)\) st step.
Thus, if we can take step \(k_0\), we can (by the inductive step) take step \(k_0+1\). And since we can take step \(k_0+1\),we can (again by the inductive step) take step \(k_0+2\).And so on, forever (or, if the notion of actual infinity makes you uncomfortable, as far as we want to go).
For all \(n\geq 1\),
\(1+2+3+\ldots +n=\dfrac{n(n+1)}{2}\).
Proof. Base case: When \(n=1\), the equation \(1=\dfrac{1\cdot (1+1)}{2}\) is true.
Solution
Inductive Hypothesis: Assume that there exists a \(n\) such that whenever \(k \leq n\), the equation
\[1+2+3+\ldots +k=\dfrac{k(k+1)}{2} \label{\PageIndex{1}}\]
is true.
Inductive Step: Our goal is to show that \(P(n+1)\) is true. That is, we wish to establish that
\[1+2+3+\ldots +n+(n+1)=\dfrac{(n+1)((n+1)+1)}{2}\label{\PageIndex{2}}\]
We begin on the left-hand side of \( \ref{\PageIndex{1}}\) where we may apply the inductive hypothesis to see that
\[1+2+3+\ldots +n+(n+1)=\left[\dfrac{n(n+1)}{2}\right]+(n+1).\label{\PageIndex{3}}\]
Through the use of straightforward algebra, the right-hand side becomes
\[\dfrac{n(n+1)}{2}+\dfrac{2(n+1)}{2}=\dfrac{n(n+1)+2(n+1)}{2}=\dfrac{(n+1)(n+2)}{2}. \label{\PageIndex{4}}\]
Putting \(\ref{\PageIndex{3}}\) and \(\ref{\PageIndex{4}}\) together, we obtain
\(1+2+3+\ldots +n+(n+1)=\dfrac{(n+1)((n+1)+1)}{2},\)
which is exactly the goal we stated in \(\ref{\PageIndex{2}}\).
We conclude with opportunities to practice induction.
For all \(k\geq 1\), \(k\geq 1\), \(3^k>k\).
Prove that the sum of the first \(\mathbb{N}\) cubes is \(\dfrac{n^2(n+1)^2}{4}\). That is,
\(1^3+2^3+3^3+\ldots +n^3=\dfrac{n^2(n+1)^2}{4}\).
(Bernoulli's Inequality). Given a real number \(b>−1\), \(b>−1\), \((1+b)^n\geq 1+bn\) for all \(n\in \mathbb{N}_0\).


24.5: Metabolic States of the Body
Learning Objectives
- Describe what defines each of the three metabolic states
- Describe the processes that occur during the absorptive state of metabolism
- Describe the processes that occur during the postabsorptive state of metabolism
- Explain how the body processes glucose when the body is starved of fuel
The Postabsorptive State
The postabsorptive state , or the fasting state, occurs when the food has been digested, absorbed, and stored. You commonly fast overnight, but skipping meals during the day puts your body in the postabsorptive state as well. During this state, the body must rely initially on stored glycogen . Glucose levels in the blood begin to drop as it is absorbed and used by the cells. In response to the decrease in glucose, insulin levels also drop. Glycogen and triglyceride storage slows. However, due to the demands of the tissues and organs, blood glucose levels must be maintained in the normal range of 80–120 mg/dL. In response to a drop in blood glucose concentration, the hormone glucagon is released from the alpha cells of the pancreas. Glucagon acts upon the liver cells, where it inhibits the synthesis of glycogen and stimulates the breakdown of stored glycogen back into glucose. This glucose is released from the liver to be used by the peripheral tissues and the brain. As a result, blood glucose levels begin to rise. Gluconeogenesis will also begin in the liver to replace the glucose that has been used by the peripheral tissues.
After ingestion of food, fats and proteins are processed as described previously; however, the glucose processing changes a bit. The peripheral tissues preferentially absorb glucose. The liver, which normally absorbs and processes glucose, will not do so after a prolonged fast. The gluconeogenesis that has been ongoing in the liver will continue after fasting to replace the glycogen stores that were depleted in the liver. After these stores have been replenished, excess glucose that is absorbed by the liver will be converted into triglycerides and fatty acids for long-term storage. Figure \(\PageIndex{2}\) summarizes the metabolic processes occurring in the body during the postabsorptive state.
Starvation
When the body is deprived of nourishment for an extended period of time, it goes into “survival mode.” The first priority for survival is to provide enough glucose or fuel for the brain. The second priority is the conservation of amino acids for proteins. Therefore, the body uses ketones to satisfy the energy needs of the brain and other glucose-dependent organs, and to maintain proteins in the cells (see [link]). Because glucose levels are very low during starvation, glycolysis will shut off in cells that can use alternative fuels. For example, muscles will switch from using glucose to fatty acids as fuel. As previously explained, fatty acids can be converted into acetyl CoA and processed through the Krebs cycle to make ATP. Pyruvate, lactate, and alanine from muscle cells are not converted into acetyl CoA and used in the Krebs cycle, but are exported to the liver to be used in the synthesis of glucose. As starvation continues, and more glucose is needed, glycerol from fatty acids can be liberated and used as a source for gluconeogenesis.
After several days of starvation, ketone bodies become the major source of fuel for the heart and other organs. As starvation continues, fatty acids and triglyceride stores are used to create ketones for the body. This prevents the continued breakdown of proteins that serve as carbon sources for gluconeogenesis. Once these stores are fully depleted, proteins from muscles are released and broken down for glucose synthesis. Overall survival is dependent on the amount of fat and protein stored in the body.
Chapter Review
There are three main metabolic states of the body: absorptive (fed), postabsorptive (fasting), and starvation. During any given day, your metabolism switches between absorptive and postabsorptive states. Starvation states happen very rarely in generally well-nourished individuals. When the body is fed, glucose, fats, and proteins are absorbed across the intestinal membrane and enter the bloodstream and lymphatic system to be used immediately for fuel. Any excess is stored for later fasting stages. As blood glucose levels rise, the pancreas releases insulin to stimulate the uptake of glucose by hepatocytes in the liver, muscle cells/fibers, and adipocytes (fat cells), and to promote its conversion to glycogen. As the postabsorptive state begins, glucose levels drop, and there is a corresponding drop in insulin levels. Falling glucose levels trigger the pancreas to release glucagon to turn off glycogen synthesis in the liver and stimulate its breakdown into glucose. The glucose is released into the bloodstream to serve as a fuel source for cells throughout the body. If glycogen stores are depleted during fasting, alternative sources, including fatty acids and proteins, can be metabolized and used as fuel. When the body once again enters the absorptive state after fasting, fats and proteins are digested and used to replenish fat and protein stores, whereas glucose is processed and used first to replenish the glycogen stores in the peripheral tissues, then in the liver. If the fast is not broken and starvation begins to set in, during the initial days, glucose produced from gluconeogenesis is still used by the brain and organs. After a few days, however, ketone bodies are created from fats and serve as the preferential fuel source for the heart and other organs, so that the brain can still use glucose. Once these stores are depleted, proteins will be catabolized first from the organs with fast turnover, such as the intestinal lining. Muscle will be spared to prevent the wasting of muscle tissue; however, these proteins will be used if alternative stores are not available.
Review Questions
Q. During the absorptive state, glucose levels are ________, insulin levels are ________, and glucagon levels ________.
A. high; low; stay the same
B. low; low; stay the same
C. high; high; are high
D. high; high; are low
Answer: D
Q. Starvation sets in after 3 to 4 days without food. Which hormones change in response to low glucose levels?
A. glucagon and insulin
B. ketones and glucagon
C. insulin, glucose, and glucagon
D. insulin and ketones
Answer: A
Q. The postabsorptive state relies on stores of ________ in the ________.
A. insulin; pancreas
B. glucagon; pancreas
C. glycogen; liver
D. glucose; liver
Answer: C
Critical Thinking Questions
Q. In type II diabetes, insulin is produced but is nonfunctional. These patients are described as “starving in a sea of plenty,” because their blood glucose levels are high, but none of the glucose is transported into the cells. Describe how this leads to malnutrition.
A. Insulin stimulates the uptake of glucose into the cells. In diabetes, the insulin does not function properly; therefore, the blood glucose is unable to be transported across the cell membrane for processing. These patients are unable to process the glucose in their blood and therefore must rely on other sources of fuel. If the disease is not controlled properly, this inability to process the glucose can lead to starvation states even though the patient is eating.
Q. Ketone bodies are used as an alternative source of fuel during starvation. Describe how ketones are synthesized.
A. When triglycerides and fatty acids are broken down, acetyl CoA is created. If excess acetyl CoA is generated in this process, the excess is used in ketogenesis or the creation of ketones. This creation results from the conversion of acetyl CoA by thiolase into acetoacetyl CoA. This acetoacetyl CoA is subsequently converted into β-hydroxybutyrate, the most common ketone in the body.
Glossary
- absorptive state
- also called the fed state; the metabolic state occurring during the first few hours after ingesting food in which the body is digesting food and absorbing the nutrients
- glycogen
- form that glucose assumes when it is stored
- insulin
- hormone secreted by the pancreas that stimulates the uptake of glucose into the cells
- postabsorptive state
- also called the fasting state; the metabolic state occurring after digestion when food is no longer the body’s source of energy and it must rely on stored glycogen