Question

A population of bacteria is growing according to the model P = 100 e .60t , where P is the number of colonies and t is measured in hours. After how many hours will 400 colonies be present? Round to the nearest tenth. Use LaTeX: A=pe^{rt}A = p e r t
Group of answer choices

About 2.3 hours

About 0.6 hours

About 4.6 hours

About 8.5 hours

Answer 1

Answer:

The answer is 2.3

Explanation:

The model for the population of bacteria is growing by

P= 100 x e^.60t

where P is the number of colonies and t is measured in hours.

Now, we need to find after how many hours will 400 colonies be present

So, Putting value of P = 400 in the above model and obtain the value of t

-> 400 = 100 x e ^.60t

-> 4 = e^.60 t

Take the natural log of ln on both sides

--> ln 4 = ln e ^.60 t

--> ln 4 = .60t

t= ln 4 / .60

T= 2.3