A company determines that if x thousand dollars are spent on advertising a certain product, then S(x) units of the product will be sold, where $S(x)=-2 x^{3}+27 x^{2}+132 x+207$ for $0 \leq x \leq 17.$ a. Sketch the graph of S(x). b. How many units will be sold if nothing is spent on advertising? c. How much should be spent on advertising to maximize sales? What is the maximum sales level?

How does an understanding of advertising help you become a smarter consumer?

A city recreation department plans to build a rectangular playground 3,600 square meters in area. The playground is to be surrounded by a fence. Express the length of the fencing as a function of the length of one of the sides of the playground, draw the graph, and estimate the dimensions of the playground requiring the least amount of fencing.

Dom, the manager of a fishery, determines that t weeks after 300 fish of a particular species are released into a pond, the average weight of an individual fish (in pounds) for the first 10 weeks will be $w(t)=3+t-0.05 t^{2}.$ Dom further determines that the proportion of the fish that are still alive after t weeks is given by $p(t)=\frac{31}{31+t}.$ a. The expected yield Y(t) of the fish after t weeks is the total weight of the fish that are still alive. Express Y(t) in terms of w(t) and p(t), and sketch the graph of Y(t) for $0 \leq t \leq 10.$ b. When should Dom expect the yield Y(t) to be maximized? What is the maximum yield?

A chapter in the book discusses appeal characteristics in advertising. Use Google Videos or Google Images to find examples of the advertisements for either Xerox’s 2010 or 2013 advertising campaign. Evaluate those advertisements based on

Message structure characteristics

The functions f(x, y)=x$^2$+y$^2$ and g(x, y)=x$^2$-y$^2$ both have a critical point at (0,0). How is the behavior of the two functions at the critical point different?

Define nostalgia, and explain why it's such a widely used advertising strategy.

All gases
(a) have high densities.
(b) have no definite shape or volume.
(c) are lighter than air.
(d) exhibit similar chemical behavior.

Describe the end behavior of the graph of the polynomial function by completing the statements $f(x) \rightarrow$ ? as $x \rightarrow-\infty$ and $f(x) \rightarrow$ ? as $x \rightarrow+\infty$.

$$f(x)=x^4-7 x^2+2$$

A chapter in the book discusses stimulus factors in advertising. Use Google Videos or Google Images to find examples of the advertisements for Ford Fiesta’s advertising campaigns. Evaluate those advertisements based on the following stimulus factors:

Information quantity

For the rational functions in the following exercise, find all zeros and vertical asymptotes and describe the long-run behavior, then graph the function.

$$y=\frac{x+3}{x+5}$$

________ is when you take away a pleasant stimulus to stop a behavior.
a. positive reinforcement
b. negative reinforcement
c. positive punishment
d. negative punishment

Using an example of your own, explicitly convert some string to a list. Describe, in your own words, the behavior of the list constructor on a string input.

Graph the function and its derivative together. Comment on the behavior of $f$ in relation to the signs and values of $f^{\prime}$.

$$f(x)=\sin 2 x, \quad 0 \leq x \leq \pi$$