3. Consider the equation $\frac{dz}{dt} = -z^5 + 4z^4 + 12z^3$
a. Create a phase-line diagram for the equation and classify each critical number as stable, unstable, or
semistable.
b. Sketch a possible solution of $\frac{dz}{dt} = -z^5 + 4z^4 + 12z^3$; $z(0) = 1$. Label the axes, show appropriate
scaled and any asymptotes.
4. Suppose the equation $P' = 0.5P(1000 - 1.6P)$ models the growth of a population. If $P(0) = 700$, what
happens to the population over a long period of time? [Hint: You do not need to actually solve the equation to
answer this.]
