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? Assume that the population decreases according to the exponential model.
A)2000
B)5281
C)5061
D)2641

Question

Quizplus · Accepted Answer

The exponential decay model is given by $P(t) = P_0e^{rt}$, where $P(t)$ is the population at time $t$, $P_0$ is the initial population, $r$ is the rate of decay, and $t$ is the time. Given $P_0 = 10000$ and $P(8) = 6000$, we can find $r$ by solving $6000 = 10000e^{8r}$. This gives $r = \frac{\ln(0.6)}{8}$. To find the population at $t = 10$, we substitute $r$ and $t = 10$ into the model: $P(10) = 10000e^{10\frac{\ln(0.6)}{8}}$, which calculates to approximately 5281.

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