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

kislotd

Answered question

2022-08-01

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?

Answer & Explanation

Coleman Ali

Coleman Ali

Beginner2022-08-02Added 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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