Consider the differential equation dP/dt=P (P−1) (2−P) which represents the rate of change in the population of Minks where the population (in thousands) can be described in terms of time t. (a) Based on the equilibrium solutions make a rough sketch of possible solution curves. (b) If P(0)=1.5, describe the solution P(t) as P→∞. (c) If P(0)=0.5, describe the solution P(t) as P→∞. (d) Can a population of 900 ever increase to 1100?

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Differential Equations:

Consider the differential equation dP/dt=P (P−1) (2−P) which represents the rate of change in the population of Minks where the population (in thousands) can be described in terms of time t.

(a) Based on the equilibrium solutions make a rough sketch of possible solution curves.

(b) If P(0)=1.5, describe the solution P(t) as P→∞.

(c) If P(0)=0.5, describe the solution P(t) as P→∞.

(d) Can a population of 900 ever increase to 1100?

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