Chapter 11.2, Problem 45E

Sales decay After the end of an advertising campaign, the sales of a product are given by

$S=100,000e^{-0.5t}$ where S is weekly sales in dollars and t is the number of weeks since the end of the campaign.

(a) Find the rate of change of S (that is, the rate of sales decay).

(b) From looking at the function and its derivative, explain how you know sales are decreasing.