Set up a differential equation used to model a population with logistic growth where t= time, P= the population at time t,k is the growth rate of the population when population is small, and L is the carrying capacity of the environment. Draw a graph of dtdP vs P. Label axes, intercepts appropriately, and where maxima/minima occur. On a graph of P vs t, draw and label all equilibrium solutions. Then draw 4 representative nonequilibrium solutions of P(t) on: where the initial population at time 0 is (a) Below 0 (b) Close to 0 but above 0 . (c) Close to the carrying capacity but below it. (d) Above the carrying capacity Your representative solutions must show the appropriate CONCAVITY. If there is an inflection point, you must LABEL and JUSTIFY why there is an inflection point