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Chapter 10: Q. 10.33 (page 1017)

Another researcher at the Center for Disease Control and Prevention, Lisa, is studying the growth of a bacteria. She starts his experiment with 50of the bacteria that grows at a rate of 15%per hour. He will check on the bacteria every 8 hours. How many bacteria will he find in 8 hours?

Short Answer

Expert verified

The researcher will find 166.0058bacteria in 8hours, if there are 50at the beginning and growing at a rate of 15% per hour.

Step by step solution

01

Step 1. Given

There are 50bacteria growing at a rate of 15%per hour.

To find the number of bacteria at the end of 8 hour.

02

Step 2. Formula for exponential growth or decay

For an original amount, A0, that grows or decays at a rate, r, for a certain time, t, the final amount, A, is:

A=A0ert

03

Step 3. Identify the values of each variable in the formula.

From the given,

A0=50r=0.15/hourt=8

04

Step 4. Substitute the values in the formula

Substitute the values in the formula:

A=A0ert=50e0.15(8)=166.0058

The bacteria after 8 hours is 166.0058

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