   Chapter 5.5, Problem 82E ### 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 bacteria population starts with 400 bacteria and grows at a rate of r(t) = (450.268)e1.12567t bacteria per hour. How many bacteria will there be after three hours?

To determine

To calculate: Thebacteria population during three hours.

Explanation

Given:

The function is r(t)=450.268e1.12567t.

Calculation:

The integral function is,

R(t)=03r(t)dt

Substitute (450.268e1.12567t) for r(t).

R(t)=03(450.268e1.12567t)dt (1)

The region lies between t=0 and t=3.

Take the consideration as follows:

u=1.12567t (2)

Differentiate both sides of the Equation (2).

du=1.12567dtdt=11.12567du

Calculate the lower limit value of u using Equation (2).

Substitute 0 for t in Equation (2).

u=1.12567(0)=0

Calculate the upper limit value of u using Equation (2).

Substitute 60 for t in Equation (2).

u=1.12567(3)=3.37701

Apply lower and upper limits for u in Equation (1).

Substitute u for (1

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