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?
Mathematics · High School · Wed Jan 13 2021
llm
Answered on
Formula Used :
P(t) = Po e^kt
Given:
Time = 30.8 minutes
P(t)/Po = 4
4 = e^k(30.8)
ln 4 = 30.8 k
K = ln4 / 30.8
K = 0.045
Now, when P(t)/Po = 5
5 = e^kt
5 = e^0.045 t
ln 5 = 0.045 t
t= ln5/0.045
t = 35.76 minutes
Hence, it will take 35.76 minutes for the population to quintuple.