   Chapter 11.2, Problem 45E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Sales decay After the end of an advertising campaign, the sales of a product are given by S = 100 , 000 e − 0.5 t 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.

(a)

To determine

To calculate: The rate of change of sales of product, represented by S=100,000e0.5t.

Explanation

Given Information:

The sales of a product are represented by the function, S=100000e0.5t, where S is the weekly sales, in dollars, and t represents the number of weeks since the end of the advertising campaign of the product.

Formula used:

The derivative of the exponential function,

ddx(ex)=ex

The simple power rule of differentiation,

ddx(xn)=nxn1

Calculation:

Consider the sales function provided, S=100000e0.5t

(b)

To determine

How one can tell that the sales are decreasing, using the derivative function.

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