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:

`P(t) = P(0)(1+r)^t`

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
`P(0) = 1500, P(t) = 1805, t = 4`

Find the hourly growth rate parameter.

`P(t) = P(0)(1+r)^t`

`1805 = 1500(1+r)^4`

`(1+r)^4 = (1805)/(1500)`

`\sqrt[4]{(1+r)^4} = \sqrt[4]{(1805)/(1500)}`

`1 + r = ((1805)/(1500))^{(1)/(4)}`

`1 + r = 1.0474`

`r = 0.0474`

0.0474*100% = 4.74%

The hourly growth rate parameter is of 4.74%