The population P of a bacteria culture is modeled by , 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) 57.5 hours
B) 9.6 hours
C) 92.7 hours
D) 94.5 hours
E) 59.3 hours

Question

The population P of a bacteria culture is modeled by  , 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) 57.5 hours 
B) 9.6 hours 
C) 92.7 hours 
D) 94.5 hours 
E) 59.3 hours

Quizplus · Accepted Answer

To find the time it takes for the population to double, we need to solve for when $P=2P_0$, where $P_0$ is the initial population.

\begin{align*}
2P_0 &= P = 11e^{-0.025t} \
e^{-0.025t} &= \frac{2P_0}{11} \
-0.025t &= \ln\left(\frac{2P_0}{11}ight) \
t &= \frac{\ln\left(\frac{2P_0}{11}ight)}{-0.025} \
t &\approx 92.7	ext{ hours}
\end{align*}

Therefore, the answer is (C) 92.7 hours rounded to the nearest tenth.

The Population P of a Bacteria Culture Is Modeled by