   Chapter 12.5, Problem 43E ### 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 Suppose that the growth of a certain population of bacteria satisfies d y d t = k y where y is the number of organisms, t is the number of hours, and k is a constant. If initially there are 10,000 organisms and the number triples after 2 hours, how long will it be before the population reaches 100 times the original population?

To determine

To calculate: The required time need to reach the population 100 time’s original population.

Explanation

Given Information:

The growth of a certain population of bacteria satisfy

dydt=ky

Where y is no. of organism, t is in number of hours, and k is a constant.

If 10,000 organism and the number triples after 2 hours.

Formula used:

The differential equation can be equivalently expressed in the form

g(y)dy=f(x)dx.

Then the equation is separable.

The solution of a separable differential is obtained by integrating both sides of the equation after the variable have been separated.

Calculation:

Consider the growth of a certain population of bacteria satisfy

dydt=ky

Here, the y is no. of organism, t is in number of hours, and k is a constant.

If 10,000 organism and the number triples after 2 hours.

Firstly, separate the above differential equation as:

dyy=kdt

Integrate the provided function as:

dyy=kdt

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