7. Consider the logistic equation where k > 0 and B > 0 are constants. Find and classify equilibrium solutions and draw a phase line. Use your work from part (a) to sketch the family of solutions corresponding to this differential equation. z-x O U'i-'D Vvv 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) Use your results from part (c) to determine the arbitrary constant if P(0) : P0. Is it possible to evaluate the itli'm POE)? If so, evaluate the limit, if not, explain why. 00