Solve the problem.
-A bacterial culture has an initial population of 10,000 . If its population declines to 6000 in 8 hours, what will it be at the end of 10 hours?
A) 5061
B) 2000
C) 5281
D) 2641

Question

Quizplus · Accepted Answer

The population decline can be modeled by an exponential decay function, $P(t) = P_0 e^{kt}$, where $P_0$ is the initial population, $P(t)$ is the population at time $t$, and $k$ is the decay constant. Given $P_0 = 10000$ and $P(8) = 6000$, we can find $k$ by solving $6000 = 10000e^{8k}$. This gives $k = \frac{\ln(0.6)}{8}$. To find the population at $t = 10$ hours, substitute $t = 10$ and $k$ into the equation, yielding $P(10) = 10000e^{10\frac{\ln(0.6)}{8}} \approx 5281$.

Solve the Problem. -A Bacterial Culture Has an Initial Population of 10,000