   Chapter 12.2, Problem 52E ### 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

# Product quality and advertising An inferior product with a large advertising budget does well when it is introduced, but sales decline as people discontinue use of the product. Suppose that the rate of weekly sales revenue is given by S ' ( t ) = 400 ( t + 1 ) 3 − 200 ( t + 1 ) 2 where S is sales in thousands of dollars and t is time in weeks.(a) Find the function that describes the weekly sales.(b) Find the sales for the first week and the ninth week.

(a)

To determine

To calculate: The function that describes weekly sales if the rate of weekly sales revenue is given by S(t)=400(t+1)3200(t+1)2.

Explanation

Given Information:

The rate of weekly sales revenue is given by,

S(t)=400(t+1)3200(t+1)2.

Where, S is sales in thousands of dollars and t is time in weeks.

Formula used:

According to the power rule of integrals,

xndx=xn+1n+1+C

Calculation:

As it is provided that the rate of weekly sales revenue is given by,

S(t)=400(t+1)3200(t+1)2

Where, S is sales in thousands of dollars and t is time in weeks.

Now, to obtain the function that describes weekly sales at, S(t), integrate the above equation with respect to t as,

S(t)=(400(t+1)3200(t+1)2)dt

Use the power rule of integrals to obtain,

S(t

(b)

To determine

To calculate: The sales for the first week and the ninth week if the rate of weekly sales revenue is given by S(t)=400(t+1)3200(t+1)2.

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