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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