The Reverse Logistic Equation Consider the logistic equation dP dt = −kP 1 − P B where k > 0 and B > 0 are constants. (a) Perform a qualitative analysis to find and classify equilibrium solutions (use a phase line). (b) Use your work from part (a) to sketch the family of solutions corresponding to this differential equation. (c) If P(t) represents a population that is governed by the reverse logistic equation, use your work in part (b) to interpret the behavior of P(t) and explain the possible fates of such a population. (d) Find an explicit expression for the particular solution for P(t) if i. 0 < P(0) < B, ii. P(0) > B, and verify that the behavior of your particular solutions is consistent with your interpretations from part (c).