Answer
A)$ P(t)=5000\cdot (0.98)^{t}$
B) $P(t)=5000\cdot (0.92)^{t}$
Work Step by Step
Given
A) We first find the percent by which the population decreases.$ r= \frac{100}{5000} = 0.02= 2\%$. The factor by which the population decreases is $b= 1-0.02= 0.98$. Hence, a model of the population is:
\begin{equation}
\begin{aligned}
P(t)&=5000\cdot (0.98)^{t}\\
\end{aligned}
\end{equation}
B)
\begin{equation}
\begin{aligned}
r&=8\% = 0.08\\
b&= 1-r= 0.92\\
a&= 5000\\
\end{aligned}
\end{equation}
The model is
\begin{equation}
\begin{aligned}
P(t)&=5000\cdot(0.92)^t\\
\end{aligned}
\end{equation}
