   Chapter 9.7, Problem 43E ### 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 An inferior product with an extensive advertising campaign does well when it is released, but sales decline as people discontinue use of the product. If the sales S (in thousands of dollars) after t weeks are given by S ( t ) = 200 t ( t + 1 ) 2 , t ≤ 0 what is the rate of change of sales when t = 9? Interpret your result.

To determine

To calculate: The rate of change of sales S=200t(t+1)2,t0, when t=9.

where t is the number of weeks.

Explanation

Given Information:

The sales are given as

S=200t(t+1)2,t0

where t is the number of weeks.

Formula used:

The rate of change of a function is given by its derivative. If a function is such that it is the ratio of two differentiable functions, then its derivative is calculated by the formula,

ddx[f(x)g(x)]=g(x)f(x)f(x)g(x)(g(x))2

Calculation:

Consider the provided statement,

The sales are given as,

S=200t(t+1)2,t0

Where, t is the number of weeks

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