# math

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?

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

posted by Steve

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