Question

The number of bacteria in a certain population increases according to a continuous exponential growth model, with a growth rate parameter of 9.4% per hour.
How many hours does it take for the size of the sample to double?
Note: This is a continuous exponential growth model.
Do not round any intermediate computations, and round your answer to the nearest hundredth.
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Answer 1

Answer:

It takes 7.37 hours for the size of the sample to double.

Step-by-step explanation:

Continuous exponential growth model:

The continuous exponential growth model for populations is given by:

$P(t) = P(0)e^{rt}$

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

Growth rate parameter of 9.4% per hour.

This means that $r = 0.094$

So

$P(t) = P(0)e^{rt}$

$P(t) = P(0)e^{0.094t}$

How many hours does it take for the size of the sample to double?

This is t for which P(t) = 2P(0). So

$P(t) = P(0)e^{0.094t}$

$2P(0) = P(0)e^{0.094t}$

$e^{0.094t} = 2$

$\ln{e^{0.094t}} = \ln{2}$

$0.094t = \ln{2}$

$t = \frac{\ln{2}}{0.094}$

$t = 7.37$

It takes 7.37 hours for the size of the sample to double.