Answer
A) $P= 3500-180t$
B) $P=3500(0.930)^t$
The percent rate is $7\% $ per year.
Work Step by Step
A)
Let $P(t)= b+mt$ represent the population of fish at time $t$.
The vertical intercept of the function is $b = 3500$. We find the slope from:
$$
m=\frac{\Delta P}{\Delta t}=\frac{1700-3500}{10-0}=-180 .
$$
The required formula is
$$
P= 3500-180t
$$
B)The vertical intercept of the function is $b = 3500$ and so
$P(t)= 3500(b)^t$. Use the point (10,1700) to find the value of $b$.
$$
\begin{aligned}
3500(b)^{16}& =1700 \\
b^{10} & =\frac{1700}{3500}\\
b & =\left(\frac{1700}{3500}\right)^{1 / 10}=0.930
\end{aligned}
$$
The required formula is
$$
P=3500(0.930)^t
$$
The percent rate is $r=1-0.93= 0.07=7\% $.
C) See the figure below.
