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, and resulted in 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
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, and resulted in 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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