Answer
Model:$\quad P=180(1.01087)^{t}$
Work Step by Step
Exponential models have the the form: $P=Ab^{t}$
Given the points on the graph
$(0,180)\quad\Rightarrow\quad\left\{\begin{array}{l}
180=Ab^{0}\\
A=180\\
P=180b^{t}
\end{array}\right.$
$(50,309) $, which is 50 years after 1960 $\left\{\begin{array}{l}
309=180b^{50}\\
b^{50}=309/180\\
b=(309/180)^{1/50}\\
b\approx 1.01086630256\\
b\approx 1.01087
\end{array}\right.$
(to six significant digits.)
Thus, we have the model:
$\quad P=180(1.01087)^{t}$
