   Chapter 11.2, Problem 4CP ### 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

# If the sales of a product are given by S = 1000 e − 0.2 x , where x is the number of days after the end of an advertising campaign, what is the rate of change in sales 20 days after the end of the campaign?

To determine

To calculate: The rate of change in the sales of the product, 20 days after the end of the advertisement campaign.

Explanation

Given Information:

The sales of a product are represented by the function S=1000e0.2x.

The number of days after the end of an advertisement campaign for the product is represented by x. It has been 20 days after the end of the campaign.

Formula used:

If f(x)=cu(x), where, c is a constant and u(x) is a differentiable function of x, then,

f(x)=cu(x)

Where, u is a differentiable function of x,

According to the property of derivatives, if y=ex,

dydx=ex

According to the power rule of differentiation,

dydx=nxn1

Calculation:

Consider the sales function provided,

S=1000e0.2x

Differentiate both sides with respect to x,

S=ddx(1000e0.2x)=1000ddx(e0

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