Chapter 5.1, Problem 46E

Advertising and sales Suppose that sales are related to advertising expenditures according to one of the following two models, where $S_1\text{and }{S}_n$ are sales and x is advertising, all in millions of dollars.

$\begin{array}{l}{S}_1=30+20x-0.4x^2\\ S_n=24.58+325.18\left(1-e^{-x/14}\right)\end{array}$

(a) Graph both of these functions on the same set of axes. Use a graphing utility.

(b) Do these two functions give approximately the same sales per million dollars of advertising for $0\le x\le 20$?

(c) How do these functions differ for $x>20$? Which more realistically represents the relationship between sales and advertising expenditures after $20 million is spent on advertising? Why?