   Chapter 6.2, Problem 56E

Chapter
Section
Textbook Problem

Bacteria Growth The number of bacteria in a culture is increasing according to the law of exponential growth. There are 125 bacteria in the culture after 2 hours and 350 bacteria after 4 hours.(a) Find the initial population.(b) Write an exponential growth model for the bacteria population. Let t represent the time in hours.(c) Use the model to determine the number of bacteria after8 hours.(d) After how many hours will the bacteria count be 25,000?

(a)

To determine

To calculate: The initial population of bacteria in a culture.

Explanation

Given:

Number of bacteria is increasing according to law of exponential growth in a culture. 125 bacteria are there in the culture, after 2 hours and 350 after 4 hours.

Formula used:

We can use the exponential growth model y=Cekt

Calculation:

Let us consider the expression y=Cekt ……. (1)

In which, C is initial population of bacteria and y will be the new population and t is the time in hours.

We have, when t=2 then y=125

If we put the above values in equation 1, we get,

y=Cekt125=Cek2C=125e2k

And also,

If t=4, then y=350, C=125e2k

By again putting these values in equation 1, we get

y=Cekt

(b)

To determine

To calculate: An exponential growth model for bacteria population in a culture which is increasing according to the law of exponential growth.

(c)

To determine

To calculate: By using the exponential growth model, the number of bacteria after 8 hours in a culture.

(d)

To determine

To calculate: The time in number of hours after which the bacteria count will become 25,000.

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