The population P of a bacteria culture is modeled by $P = 4100 e ^ { k t }$ ,where t is the time in hours.If the population of the culture was 5800 after 40 hours,how long does it take for the population to double? Round to the nearest tenth of an hour.
A)54.8 hours
B)8.9 hours
C)79.9 hours
D)81.7 hours
E)56.6 hours

Question

Quizplus · Accepted Answer

To find out how long it takes for the population to double, we need to solve for the time t when P = 2P₀ (where P₀ is the initial population).

2P₀ = P₀e^(0.15t)
2 = e^(0.15t)
0.15t = ln(2)
t = ln(2)/0.15 ≈ 79.9

Therefore, it takes approximately 79.9 hours for the population to double. The best choice is C.

The Population P of a Bacteria Culture Is Modeled By P