Question

A population of bacteria is growing according to the exponential model P = 100e.70t, where P is the number of colonies and t is measured in hours. After how many hours will 300 colonies be present? [Round answer to the nearest tenth.]

A) 0.7
B) 1.6
C) 5.7
D) 7.2

Answer 1

We are tasked to solve for the total number of hours given the exponential model P = 100e0.7t where P represents the calories.
P = 300
Solving for t, we have:
300 = 100e0.7t
300/100 =e0.7t
3=e0.7t
ln3 = 0.7 t
t = ln3 / 0.7
t = 1.57 hours

The answer is the letter "B" which is 1.6.