Chapter 12.2, Problem 54E

Product quality and advertising An inferior product with a large advertising budget does well when it is introduced, but sales decline as people discontinue use of the product. Suppose that the rate of weekly sales revenue is given by

$S\text{'}\left(t\right)=\frac{400}{{\left(t+1\right)}^3}-\frac{200}{{\left(t+1\right)}^2}$ where S is sales in thousands of dollars and t is time in weeks.

(a) Find the function that describes the weekly sales.

(b) Find the sales for the first week and the ninth week.