Can someone please help me with this bacteria problem

A population of bacteria is growing according to the function below, where t is in hours. How many hours will it take for the population to grow to 12,000 bacteria? Round your answer to the nearest integer. Do not include units in your answer.

B(t) = 50 x e^2t

12,000 = 50 x e^2t

=> e^2t = 240

=> 2t = ln240

i.e. t = (1/2)ln240 = 2.74 ≈ 3

:)>

B(t) = 50 x e^2t
Where B(t) is the number of bacteria at a certain time.

To find the time when the population has 12000 bacteria, let B(t) = 12 000.

Therefore,
12 000 = 50*e^2t

Now divide both sides by 50 to arrive at:
240 = e^2t

Now you take the "natural log" or "ln" of both sides, that is:
ln 240 = ln e^(2t)

Now we use the rule that ln e^(2t) = 2t.

Therefore,
ln 240 = 2t

Typing ln240 in the calculator gives 5.48
Therefore,
5.48 = 2t
Therefore,
t = 5.48/2 = 2.74 = 3 hrs when rounded.

initially
B(t = 0) = 50 bacteria!

the condition is B(t) = 12,000

so 50 x e^2t = 12,000 ---> e^2t = 240 ---> 2t = ln(240) ---> t = 2,74 ---> t = 3

12000=50*e^2t.
240=e^2t.
Ln 240=2t
5.48=2t
t=2.74

actually the answer is 2.74 hr. But round off the answer is 3.