Question

A population of bacteria is growing according to the exponential model P = 100e(.70)t, where P is the number of colonies and t is measured in hours. After how many hours will 300 colonies be present? [Round answer to the nearest tenth.]

Answer 1

For this case we have a function of the form:

`P = 100e^ {0.70t}`

Where,

• P: the number of colonies
• t: time in hours

By the time there are 300 colonies we have:

`100e ^ {0.70t} = 300`

From here, we clear the value of t.

We have then:

`e ^ {0.70t} = \frac {300} {100}\\e ^ {0.70t} = 3\\0.70t = ln (3)\\t = \frac {ln (3)} {0.70}\\t = 1.6 hours`

Answer:

after 1.6 hours 300 colonies will be present