Suppose further that the population’s rate of change is governed by the differential equation

Question

dP/dt = f(P)
where f (P) is the function graphed.
For which values of the population P does the population increase?
(b) For which values of the population P does the population decrease?
(c) If P(0) = 3, how will the population change in time?
(d) If the initial population satisÆes 0 < P(0) < 1, what will happen to the
population after a very long time?
(e) If the initial population satisfies 1 < P(0) < 3, what will happen to the
population after a very long time?
(f) If the initial population satisfies 3 < P(0), what will happen to the population
after a very long time?
(g) This model for a population’s growth is sometimes called “growth with a
threshold.” Explain why this is an appropriate name.

Answer 1

Sorry, no graphs here.
But you know that since f(P) is dP/dt, when f is positive, P is increasing.

As for the other items, no idea, since no picture is available.

Sounds like P is some kind of exponential or logistic model. Better review those topics.