   Chapter 9.6, Problem 48E ### 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

# Advertising and sales The daily sales S (in thousands of dollars) 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. What is the rate of change of sales at (a) t = 8? (b) t = 10?(c) Should the campaign be continued after the 10th week? Explain.

(a)

To determine

To calculate: The rate of change of sales at t=8. The daily sales S (in thousands of dollars) attributed to an advertising campaign are given by S=1+3t+318(t+3)2 where t is the number of weeks the campaign runs.

Explanation

Given Information:

The daily sales S (in thousands of dollars) attributed to an advertising campaign are given by S=1+3t+318(t+3)2 where t is the number of weeks the campaign runs.

Formula used:

The power rule of differentiation,

ddxxn=nxn1

Calculation:

Consider the provided function,

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

Rewrite the function,

S=1+3(t+3)118(t+3)2

Consider (t+3) to be u,

S=1+3u118u2

Differentiate both sides with respect to t,

dSdt=ddt(1+3u118u2)

Simplify using the power rule,

dSdt=ddt(1)+ddt(3u1)ddt(18u2)=0+3(1)u11dudt18(2)u21dudt=3u2dudt+36u3

(b)

To determine

To calculate: The rate of change of sales at t=10. The daily sales S (in thousands of dollars) attributed to an advertising campaign are given by S=1+3t+318(t+3)2 where t is the number of weeks the campaign runs.

(c)

To determine

Whether the campaign should be continued after the 10th week. The daily sales S (in thousands of dollars) attributed to an advertising campaign are given by S=1+3t+318(t+3)2 where t is the number of weeks the campaign runs.

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