   Chapter 12, Problem 38RE ### 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

# Bacterial growth A population of bacteria grows at the rate d p d t = 100 , 000 ( t + 100 ) 2 where p is the population and t is time. If the population is 1000 when t =   1 , write the equation that gives the size of the population at any time t.

To determine

To calculate: The equation which provides the size of population at the time t. If a population of bacteria grows at the rate dpdt=100,000(t+100)2.

Explanation

Given Information:

The provided population of bacteria grows at the rate,

dpdt=100,000(t+100)2.

Where p is the population and t is time.

The population of the bacteria is 1000 when t=1.

Formula used:

According to the power rule of integrals,

ddx(xn)=xn+1n+1+C

Calculation:

Consider the rate at which the population of bacteria grows,

dpdt=100,000(t+100)2

Where p is the population and t is time.

Now, the rate of population growth can be obtained by differentiating the population function as,

P(t)=100,000(t+100)2

Thus, the population function can be obtained by integrating the above function as,

P(t)=100,000(t+100)2dx

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started 