   Chapter 9.8, Problem 41E Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340

Solutions

Chapter
Section Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340
Textbook Problem

Advertising and sales The daily sales S (in thousands of dollars) that are attributed to an advertising campaign are given by s = 1 + 3 t + 3 − 18 ( t + 3 ) 2 where t is the number of weeks the campaign runs.(a) Find the rate of change of sales at any time t.(b) Use the second derivative to find how this rate changing at t = 15.(c) Interpret your result in part (b).

(a)

To determine

To calculate: The rate of change in the sales S=1+3t+318(t+3)2 with respect to time t where t is the number of weeks the campaign runs.

Explanation

Given information:

The daily sales S (in thousands of dollars) is given as

S=1+3t+318(t+3)2

where t is the number of weeks the campaign runs.

Formula used:

The power rule for differentiation states that,

ddx(xk)=kxk1

The derivative of a constant times a function is

ddx[cf(x)]=cddx(f(x))

The derivative of a sum/difference of terms in a function,

ddx(f±g)=ddxf±ddxg

Calculation:

Consider the equation,

S=1+3t+318(t+3)2

(b)

To determine

To calculate: The second derivative of the sales S=1+3t+318(t+3)2 with respect to time t where t is the number of weeks the campaign runs and then determine the value for t=15.

(c)

To determine

The result obtained from the part (b).

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