Suppose that the number P(t) of alligators in a swamp as a function of time t in months satisfies the differential equation dP/dt = 0.01P - 0.0001P^2. In this model, the alligator population is a continuous quantity that can conceivably take any non-negative real number as a value.
a If there are initially 25 alligators, what happens to the population in the long run?
b Suppose that alligators are introduced into the swamp at a continuous rate of 0.21 alligators per month. Modify the differential equation above that incorporates this.
c What happens to the population in the long run, in this new scenario? (Assume an initial population of 25.)