Question

The rate of increase of bacteria in a culture is proportional to the number of bacteria present .if the original number of bacteria double in the two hours, in how many hours will it be five times?

Answer 1

this is exponential growth. Since it doubles in 2 hours, the population is after t hours is

p(t) = A*2^(t/2)

So, it will be 5 times as big as at first when

2^(t/2) = 5

or, you can start from scratch, using

dp/dt = kp
dp/p = k dt
lnp = kt+lnA
p = A*e^(kt)
and work it from there