The number of bacteria in a culture increases exponentially with a growth constant of 0.2 hour^-1. How long will it take for the population to increase from 4000 to 20,000 ? A) 25.00 hours B) 0.12 hour C) 8.05 hours D) 0.04 hour

Question

Quizplus · Accepted Answer

The general formula for exponential growth is N=N0e^kt, where N is the final population, N0 is the initial population, k is the growth constant, and t is the time.

Using the given values, we can write:

20,000 = 4000e^(0.2t)

Dividing both sides by 4000:

5 = e^(0.2t)

Taking the natural logarithm of both sides:

ln(5) = 0.2t

t = ln(5)/0.2

t ≈ 8.05 hours

Therefore, the correct answer is C.

The Number of Bacteria in a Culture Increases Exponentially with a Growth