Math question – Description
39. Suppose you wish to model a population with a differential equation of the form dp/dt = f(P), where P(t) is the population at time t. Experiments have been performed on the population that give the following information: • The only equilibrium points in the population are P = 0, P = 10, and P = 50. • If the population is 100, the population decreases. • If the population is 25, the population increases. (a) Sketch the possible phase lines for this system for p > 0(there are two). (b) Give a rough sketch of the corresponding functions f(P) for each of your phase lines. (c) Give a formula for functions f(P) whose graph agrees (qualitatively) with the rough sketches in part (b) for each of your phase lines.
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