Question

In a lab experiment, 590 bacteria are placed in a petri dish. The conditions are such

that the number of bacteria is able to double every 24 hours. How many bacteria

would there be after 13 hours, to the nearest whole number?

Answer 1

There would be 859 bacteria after 13 hours.

Explanation:

The population of bacteria after t hours is given by the following equation:

`P(t) = P(0)e^(rt)`

In which P(0) is the initial population and r is the growth rate.

The number of bacteria is able to double every 24 hours.

This means that
`P(24) = 2P(0)`. So

`P(t) = P(0)e^(rt)`

`2P(0) = P(0)e^(24r)`

`e^(24r) = 2`

`\ln{e^(24r)} = ln(2)`

`24r = ln(2)`

`r = (ln(2))/(24)`

`r = 0.0289`

590 bacteria are placed in a petri dish.

This means that P(0) = 590. So

`P(t) = P(0)e^(rt)`

`P(t) = 590e^(0.0289t)`

How many bacteria would there be after 13 hours, to the nearest whole number?

This is P(13).

`P(t) = 590e^(0.0289t)`

`P(13) = 590e^(0.0289*13) = 859`

There would be 859 bacteria after 13 hours.