   Chapter 12.2, Problem 54E ### 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

# Franchise growth A new fast-food firm predicts that the number of franchises for its products will grow at the rate d n d t = 9 t + 1 where t is the number of years, 0 ≤ t ≤ 10 . If there is one franchise ( n =   1 ) at present ( t   =   0 ) , how many franchises are predicted 8 years from now?

To determine

To calculate: The number of franchises predicted after 8 years if number of franchises for its products will grow at the rate dndt=9t+1.

Explanation

Given Information:

Number of franchises for its products will grow at the rate,

dndt=9t+1

Where t is the number of years and n is the number of franchises.

Formula used:

According to the power rule of integrals,

xndx=xn+1n+1+C

Calculation:

As it is provided that number of franchises for its products will grow at the rate,

dndt=9t+1

Where t is the number of years and n is the number of franchises.

Now, the function for number of franchises can be obtained by integrating the above rate equation with respect to t as,

dndtdt=9t+1dt

Now, integrate the above function using power rule of integrals as,

dndtdt=9t+1dtn(t)=9(t+1)

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