A colony of bacteria originally contains 400 bacteria. It doubles in size every 30 minutes. How many hours will it take for the colony to contain 4,000 bacteria?

kislotd 2022-08-01 Answered
A colony of bacteria originally contains 400 bacteria. It doubles in size every 30 minutes. How many hours will it take for the colony to contain 4,000 bacteria?
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Answers (1)

Coleman Ali
Answered 2022-08-02 Author has 13 answers
Recall the following population growth formula:
P = P 0 e r t
Here, P reresents the total population after time t, P 0 represents the initial population and r represents the rate of growth.
Given,
P 0 = 400 t = 30  min = 1 2  hours P = 2 P 0
Substitute the given values in the above-mentioned formula as,
2 P 0 = P 0 e 1 2 r 2 = e r 2 ln 2 = r 2 ln e r = 2 ln 2
This gives r = 2 ln 2
Now, calculate the required time when population reaches 4000 as,
4000 = ( 400 ) e 2 ( ln 2 ) t e ( 2 ln 2 ) t = 4000 400 e ( 2 ln 2 ) t = 10 l n e ( 2 ln 2 ) t = ln 10 ( 2 ln 2 ) t = ln 10 t = ln 10 2 ln 2 = 1.7
Therefore, it takes 1.7 hours for the colony to contain 4000 bacteria.
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