   Chapter 3.8, Problem 1E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# A population of protozoa develops with a constant relative growth rate of 0.7944 per member per day. On day zero the population consists of two members. Find the population size after six days.

To determine

To find: The population size after six days.

Explanation

Given:

The constant relative growth rate is k=0.7944.

Theorem used:

“The only solutions of the differential equation dydt=ky are the exponential functions

y(t)=y(0)ekt.”

Calculation:

Obtain the population size after six days.

Let P(t) be the population of protozoa after t days and it develops with a constant relative rate. That is, dPdt=kP with p(0)=2.

Use theorem sated above, p(t)=p(0)ekt

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