3. Consider the autonomous first order ODE, P'(t) = P(P? 8P + 15), for modeling population dynamics where P(t) > 0 is the population at time t. (a) Draw the one-dimensional phase portrait (phase line analysis) on the vertical (P) axis provided in the figure below. Identify the equilibrium solutions (constant solutions) and the direction of the solution (increasing or decreasing) in each region of the phase line, for increasing t. Classify each equilibrium solution as either asympotically stable, unstable or semi-stable. (b) In the same figure, draw the equilibrium solutions from part (a) as functions over t, for t > 0. Then sketch approximate solution curves P(t) satisfying initial conditions P(O) = -0.5, P(0) = 2, P(0) = 4 and P(O) = 5.5. (c) Determine the value(s) of P at which the solutions have an inflection point. This can be calculated directly from the ODE. 3. Consider the autonomous first order ODE, P'(t) = P(P? 8P + 15), for modeling population dynamics where P(t) > 0 is the population at time t. (a) Draw the one-dimensional phase portrait (phase line analysis) on the vertical (P) axis provided in the figure below. Identify the equilibrium solutions (constant solutions) and the direction of the solution (increasing or decreasing) in each region of the phase line, for increasing t. Classify each equilibrium solution as either asympotically stable, unstable or semi-stable. (b) In the same figure, draw the equilibrium solutions from part (a) as functions over t, for t > 0. Then sketch approximate solution curves P(t) satisfying initial conditions P(O) = -0.5, P(0) = 2, P(0) = 4 and P(O) = 5.5. (c) Determine the value(s) of P at which the solutions have an inflection point. This can be calculated directly from the ODE