Question

The number N of bacteria present in a culture at time t (in hours) obeys the equation N = 1000e^0.01t After how many hours will the population equal 1500? 2000?​

Answer 1

Answer: N(t) = (2^t)*1500

Step-by-step explanation:

Let's define the hour "zero" as the initial population.

So if N(t)  is the number of bacteria after t hours, then:

N(0) = 1500.

Now, we know that the population doubles every hour, so we will have that after one hour, at t = 1

N(1) = 2*1500 = 3000

after two hours, at t = 2.

N(2) = 2*(2*1500) = (2^2)*1500

After three hours, at t = 3

N(3) = 2*(2^2)*1500 = (2^3)*1500

So we already can see the pattern, the number of bacteria after t hours will be:

N(t) = (2^t)*1500