Question

Suppose that the number of bacteria in a certain population increases according to a continuous exponential growth model. A sample of 1500 bacteria selected

from this population reached the size of 1805 bacteria in four hours. Find the hourly growth rate parameter.
Note: This is a continuous exponential growth model.
Write your answer as a percentage. Do not round any intermediate computations, and round your percentage to the nearest hundredth.
00
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Answer 1

The hourly growth rate parameter is of 4.74%

Explanation:

Continuous growth model:

The continuous growth model for a population after t hours is given by:

In which P(0) is the initial population and r is the hourly growth rate parameter, as a decimal.

A sample of 1500 bacteria selected from this population reached the size of 1805 bacteria in four hours.

This means that

Find the hourly growth rate parameter.

0.0474*100% = 4.74%

The hourly growth rate parameter is of 4.74%