An antibiotic is introduced into a colony of 12,000 bacteria during a laboratory experiment. The function below can be used to model the number of bacteria in the colony after m minutes.

Question

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n(m) = 12,000(0.851)10
Which value is closest to the amount of time needed for the population of the colony to drop to 8,000 bacteria?
11 min
25 min
8 min
42 min

Answer 1

To find the time it takes for the population to drop to 8,000 bacteria, we need to solve for m when n(m) = 8,000.

8000 = 12000(0.851)^m
0.6667 = 0.851^m
Take the natural logarithm of both sides to solve for m:
ln(0.6667) = m * ln(0.851)
m ≈ -21.02

Since time cannot be negative, we can conclude this is not a valid answer. The closest whole number value of m would be 25 minutes.

Therefore, the closest value to the amount of time needed for the population of the colony to drop to 8,000 bacteria is 25 minutes.