Question

During the exponential phase, E. coli bacteria in a culture increase in number at a rate proportional to the current population. If the population quadruples in 30.8 minutes, in how many minutes will the population quintuple?

Answer 1

The exponential function is given by P(t) = P0 e^kt; where P(t) is the current population, P0 is the initial population and t is the time.
Thus, P(t) / P0 = e^kt
4 = e^30.8k
ln 4 = 30.8k
k = ln 4 / 30.8 = 0.045

For the population to quituple,
5 = e^0.045t
ln 5 = 0.045t
t = ln 5 / 0.045 = 35.76

Therefore, it will take the population 35.76 minutes to quintuple.