\begin{equation*}
\frac{dP}{dt} = P\left(1 - \frac{P}{200} \right) - 32 = -\frac{1}{200}(P - 40)(P - 160)
\end{equation*}
is an autonomous differential equation, the direction field does not depend on
\(t\text{.}\) Consequently, we need only keep track of what happens on the vertical axis. We can do this with a
phase line. Instead of drawing the entire direction field, we can draw a single line containing the same information (
Figure 1.3.10).