math word problem

Question

The number of bacteria in a certain sample increases according to the following function, where y0

 is the initial number present, and y

 is the number present at time t

 (in hours).

y=y0^e0.059t

How many hours does it take for the size of the sample to double? Do not round any intermediate computations, and round your answer to the nearest tenth.

Answer 1

For the size to double, y = 2y₀

y = y₀e^0.059t

2y₀ = y₀e^0.059t

2 = e^0.059t

Ln2 = Lne^0.059t

Ln2 = 0.059t Lne

But Lne = 1

t = Ln2 /0.059

t = 11.7 years