Answer
$
p(t)=1149.61\left( 0.93504\right)^x
$
Work Step by Step
We want to find $p(t)=ab^x$, given $p(20)=300$ and $p(50)=40$.
We now find $b$ and $a$.
$$
a b^{20}=300 \quad \text { and } \quad a b^{50}=40
$$ $$
\begin{aligned}
&\frac{a b^{50}}{a b^{20}}=\frac{40}{300}\\
&\begin{aligned}
b^{30} & =\frac{4}{30} \\
b & =\left(\frac{4}{30}\right)^{\frac{1}{30}}\approx 0.93504
\end{aligned}
\end{aligned}
$$
and
$$
\begin{aligned}
a b^{50} & =40 \\
a & =\frac{40}{b^{50}}\approx 1149.61
\end{aligned}
$$
Hence
$$
p(t)=1149.61\left( 0.93504\right)^x
$$
