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A biologist finds that the population of a certain type of bacteria doubles each half-hour. An initial culture has 90 bacteria.
-How long will it take for the number of bacteria to reach 245,760?
A) 5.5 hours
B) 6 hours
C) 6.5 hours
D) 7 hours

Question

Quizplus · Accepted Answer

To solve this problem, we need to use exponential growth formula:

N(t) = N0 x 2^(t/k)

where N(t) is the number of bacteria at time t, N0 is the initial number of bacteria, k is the doubling time (30 minutes in this case), and t is the time elapsed.

We want to find the time it takes for the population to reach 245,760, which is four doublings from the initial population of 90:

N(t) = N0 x 2^4 = 90 x 16 = 1440

N(t) = N0 x 2^(t/k)

245,760 = 90 x 2^(t/30)

2,730 = 2^(t/30)

t/30 = log2(2,730)

t ≈ 90.42 minutes ≈ 1.51 hours

Therefore, it will take about 6 hours for the number of bacteria to reach 245,760.

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