dP/dt= .0004P (P-150)
a) Find the equilibrium solutions, draw the phase line and classify critical points.
b) If P(0)=200, solve this IVP and show all the steps. Find P(t) explicitly and draw its graph. There is a value of t=tdoom where as t-->tdoom, there is a population explosion. Find this value of t.
c) If P(0)=100, find again P(t) explicitly and draw its graph. Determine the behavior of P(t) as t→∞ and write a sentence drawing the appropriate conclusion.