Listed below are three examples of rational functions used to model particular situations. While the applications are not related, you will discover that the functions all exhibit a similar behavior.

In many situations, a model is approximate. In the first two examples below, the functions were derived empirically, meaning they were determined by considering the actual, real-world results of a similar activity in the past. The model approximates what would happen in a future, similar situation.

Other models, like the third example below, may be exact relations determined by known, fixed material and labor costs. That is, for physically meaningful values of n – you cannot make a negative number of DVDs or an infinite number of DVDs – the output C(n) is exact.

Also, a model is often limited in its applicability. You will see this in all three of these examples, and the implications of these limitations will be a part of the resulting discussion.

In the following examples, each function has a denominator, making them all rational functions, and so the denominator becoming zero has to be avoided because dividing by zero is undefined, or not allowed.

1. The cost C(x), in thousands of dollars, to remove x percent of a particular toxic pollutant from a certain river is modeled by:
2. The cost C(x), in thousands of dollars, to inoculate x percent of the population of a large city against a strain of the flu is modeled by the rational function:
3. The cost C(n), in dollars per dvd, for a particular company to manufacture n copies of a certain DVD is given by:
4. Note: It is standard to use n as the independent variable name when the variable must be an integer.

Assignment, please do the following:

For your initial post, please do the following:

1. Choose one of the rational functions in the examples given above.
2. Select eight values of the independent variable for your chosen function, and then compute the corresponding output of the function. Show your calculations. 

• For examples 1 and 2, use this random number generator (Links to an external site.)Links to an external site. to select your x-values. This will assure you’ve chosen a variety of values so your calculations will give you an idea of the range of the function. Make sure to specify Generate 8 random integers with a value between 1 and 100. 
• For example 3, the random number generator is less useful. Just be sure to include some large numbers. 

1. For your chosen rational function, plot the eight data points you computed in (2) and then plot the entire function so that the graph passes through the points you plotted. This will require that you specify the window of your graph.

• For examples 1 and 2, the specified window of your graph should include all the possible values of the independent variable x. You will not be able to include all y values (you will see why), but specify the range of the y-axis so that you can see what happens when x is close to 100.
• For example 3, you cannot include all possible values of the independent variable x. But extend the x-axis out far enough to see what happens as x gets increasingly large.

1. In your post:

a.                  Show your calculations from part (2).

b.                 Describe what the graph tells you about your corresponding example problem.

c.                  Finally, insert the image of your graph (see instructions above).

http://www.desmos.com/calculator

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Listen to, watch or read three advertisements. Analyse the ads carefully and identify the probable promotional objective of each advertisement. If an ad focuses on discounts, the likely promotional objective is to stimulate demand. Explain why you have arrived at these conclusions. Do you think the organisations responsible for the ads have used the right medium to fulfil their objectives? Explain. (50–75 words per advertisement)

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LISTEN TO THE RECORDING ON THE ATTACHMENT BOX TO WIRTE THIS REFLECTION PAPER 

Request an informational interview with an individual about his or her career. The person you interview should not be related to you and must work in one of the industries reflected in one of your Life Design Plans. 

Utilize this Informational Interview Guide to frame your interview. 

Your reflection should be a minimum of 600 words and include the following information: 

• Which Life Design Plan the interview reflects
• The individual’s name, job title and place of employment
• Brief educational background and work history
• One thing you liked about the career or job duties
• One thing you disliked about the career or job duties
• A minimum of one other thing you learned about the position or industry
• What, if anything surprised you or was different about the job than you expected

The individual you interviewed must email Melissa  () using his or her work email address to verify you spoke with them.  YOU WILL RECEIVE A ZERO FOR THIS ASSIGNMENT IF THE INDIVIDUAL INTERVIEWED DOES NOT COMPLETE THIS EMAIL VERIFICATION. 

Reminder: Students should submit their Informational Interview #1 Topic by Sept. 27 to avoid losing 10 points on this assignment.

We highly recommend you express your appreciation to the person you interviewed by sending a hand-written thank you note or a thank you email after your interview. 

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Listen to the podcast, Speaking of Psychology: Disciplining Children Effectively.

Based on the information from the podcast, what is the take home message for parents? Support your post with theory or research that includes peer reviewed scholarly references. What relevant considerations (e.g., culture, gender, SES) seem to have been omitted or not considered in the podcast or based on your reading? What are the barriers to (or possible negative consequences of) applying the approaches suggested in this week’s readings?

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Listen to the first episode of the podcast series “Deporting Ottoman Americans” (Episode 370, released on 8/9/18):https://soundcloud.com/ottoman-history-podcast/deporting-ottoman-americans

This episode explores changes in US immigration policy before and after WWI through the question of: how do you deport someone whose state (the Ottoman Empire) no longer exists? The episode covers a range of topics. I suggest you keep an ear out for the following:

§ Which groups of people emigrated from the Ottoman Empire to the United States? When did they come and what did they do once they got here?

• §  When and why did the US end its open-borders immigration policy and implement immigration quotas?
• §  How were these immigration quotas decided? Which groups were most affected?
• §  When and why did the US start deporting immigrants back to their countries of origin?o On what basis were people deemed suitable for deportation?
• §  How does the history of race in America help explain the history of immigration anddeportation?
• §  How did changes in US immigration policy after WWI affect people who had migratedfrom the Ottoman Empire to America?You should listen to the episode, and take notes. Please do not try to answer the above questions by Googling them instead of listening to the episode, as I will be able to tell from your response whether you listened or not. After listening, you will write approximately 500 words on the following:§ What is something interesting you learned from this episode? Please explain why you find it interesting

§ How can we connect the content of this episode to the content of our class? Be sure to give specific examples from the podcast; do not use generalizations or I will assume you Googled.

This assignment will receive a 10/10 if completed to a satisfactory level, or a 0/10 (no credit) if not completed to a satisfactory level. If you receive credit, this assignment will replace your SECOND LOWEST quiz grade with a 10/10 (your lowest quiz grade out of 11 quizzes is dropped automatically.)

“Completed to a satisfactory level” means:§ You have included enough detail in your write-up to show that you listened to the

podcast and took notes

• §  You have made an effort to connect the content of the podcast to the content of ourclass.
• §  Your write-up is an adequate length (approx. 500 words)

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