Answer
a) $p(t)= 10\cdot (1.015)^t$
b) $\$13.47$.
Work Step by Step
The problem describes an exponential function with the following parameters.
\begin{equation}
\begin{aligned}
a&= 10\\
r&= 1.5\%= 0.015\\
b&=1+r = 1.015
\end{aligned}
\end{equation}
a) Hence, a model of the price of movie ticket is
\begin{equation}
\begin{aligned}
p(t)&= a\cdot b^t\\
&= 10\cdot (1.015)^t\\
\end{aligned}
\end{equation}
b) Set $t= 20$.
\begin{equation}
\begin{aligned}
p(20)&= 10\cdot (1.015)^{20}\\
&= 13.468\\
\end{aligned}
\end{equation}
The cost of movie ticket in 20 years is about $\$13.47$.
