Question

Two bacteria colonies are cultivated. The first colony has a doubling time of 2 hours and the second a doubling time of 3 hours. initially, the first colony contains 1,000 bacteria and the second colony 3,000 bacteria. At what time t will sizes of the colonies be equal?

Is doubling time = (ln2/k)?

Answer 1

Yes, that is the formula for doubling time in terms of the exponential growth facor k. But you don't need to use k to get the answer.

Populations are equal when
1000*2^(t/2) = 3000*2^(t/3)
3 = 2^[(t/2)-(t/3)] = 2^(t/6)
ln 3 = (t/6)*ln2
t/6 =ln3/ln2 = 1.58496
t = 9.51 hours