   Chapter 12.3, Problem 48E ### 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

# Population growth The rate of growth of world population can be modeled by d N d t = N 0 re r t ,    r  < 1 where t is the time in years from the present and N 0 and r are constants. What function describes world population if the present population is N 0 ?

To determine

To calculate: The world population if the present population is N0 if the rate of growth of world population can be modeled by dNdt=N0rert,r<1

Explanation

Given Information:

The rate of growth of world population can be modeled by

dNdt=N0rert,r<1

Where t is the time in year from the present and N0 and r are constant.

Formula used:

The logarithm formula is

u1u'dx=u'udu=ln|u|+C; where u is a function of x.

Calculation:

Consider the rate of growth of world population can be modeled by

dNdt=N0rert,r<1.

Let u=rt and differentiate as:

du=rdt

Integrate on both side of the provided equation as:

N(t)=N0r<

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