   Chapter 12, Problem 18T ### 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

# Suppose the rate of growth of the population of a city is predicted to be d p d t = 2000 t 1.04 where p is the population and t is the number of years past 2015. If the population in the year 2015 is 50,000, what is the predicted population in the year 2025?

To determine

To calculate: The predicted population in the year 2025 if rate of growth of the population of a city is predicted to be dpdt=2000t1.04. Here, p is the population and t is the number of years past 2018 and the population in the year 2015 is 50,000.

Explanation

Given Information:

The rate of growth of the population of a city is predicted to be dpdt=2000t1.04. Here, p is the population and t is the number of years past 2015 and the population in the year 2015 is 50,000.

Formula used:

The power rule of integration is;

The integration of function f(x)=xn is given by;

xndx=xn+1n+1+c n1

Here c is any arbitrary constant.

The sum rule is;

f(x)±g(x)dx=f(x)dx±g(x)dx

Calculation:

The rate of growth of the population of a city is predicted to be,

dpdt=2000t1.04.

The above equation can be written as;

dp=2000t1.04dt

Integrate the above expression,

dp=2000t1.04dtp=2000t1.04+11.04+1+Cp=20002

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