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The following differential equation models population changes for a harvested, logistically changing species. dPdt = 3P(1 − 1 12 P) − 8. (a) Find the equilibrium population size. (b) By thinking about the sign of the derivative, describe what happens to the population size for each of the initial conditions P(0) = 2, 4, 6, 8, 10.

The following differential equation models population changes for a harvested, logistically changing species. dPdt = 3P(1 − 1 12 P) − 8. (a) Find the equilibrium population size. (b) By thinking about the sign of the derivative, describe what happens to the population size for each of the initial conditions P(0) = 2, 4, 6, 8, 10.

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The following differential equation models population changes for a harvested, logistically changing species.
d P d t = 3 P ( 1 − 1 12 P ) − 8 .
(a) Find the equilibrium population size. (b) By thinking about the sign of the derivative, describe what happens to the population size for each of the initial conditions P ( 0 ) = 2 , 4 , 6 , 8 , 10 .

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