   Chapter 9.7, Problem 42E ### 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 Suppose that sales (in thousands of dollars) are directly related to an advertising campaign according to S = 1 + 3 t − 9 ( t + 3 ) 2 where t is the number of weeks of the campaign.(a) Find the rate of change of sales after 3 weeks.(b) Interpret the result in part (a).

(a)

To determine

To calculate: The rate of change of sales after 3 weeks for sale function S=1+3t9(t+3)2, where t is the number of weeks.

Explanation

Given Information:

The sales are given as,

S=1+3t9(t+3)2

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=1+3t9(t+3)2

where t is the number of weeks

(b)

To determine

The impact of the value of rate of change of sales after 3 weeks if the sales are given as,

S=1+3t9(t+3)2

Where, t is the number of weeks.

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