   Chapter 12.2, Problem 53E ### 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

# Demographics Because of job outsourcing, a Pennsylvania town predicts that its public school population will decrease at the rate d N d x = − 300 x + 9 where x is the number of years and N is the total school population. If the present population ( x =   0 ) is 8000, what population size is expected in 7 years?

To determine

To calculate: The expected population size in 7 years if public school population will decrease at the rate dNdx=300x+9.

Explanation

Given Information:

Public school population will decrease at the rate,

dNdx=300x+9.

Where x is the number of years and N is the total school population.

Formula used:

According to the power rule of integrals,

xndx=xn+1n+1+C

Calculation:

As it is provided that Public school population will decrease at the rate,

dNdx=300x+9

Where x is the number of years and N is the total school population.

Now, the function for public school population as a function of number of years x can be obtained by integrating the above rate equation with respect to x as,

dNdxdx=300x+9dx

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

dNdxdx=300

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