Question

Suppose that the number of bacteria in a certain population increases according to a continuous exponential growth model. A sample of 2400 bacteria selected from this population reached the size of 2892 bacteria in four hours. Find the hourly growth rate parameter.

Answer 1

Answer:
`(\ln(241/200))/(4)`

Explanation:

If
`P(t)` represents the number of bacteria after
`t` hours, then
`P(t)=2400e^(kt)`, where
`k` is the hourly growth rate parameter.

Using the fact that
`P(4)=2892`,

`2892=2400e^(4k)\\\\e^(4k)=(241)/(200)\\\\4k=\ln(241/200)\\\\k=(\ln(241/200))/(4)`