Question: A model for the population, P, of carp in a landlocked lake at time t is given by the differential equation
(dP/dt) = 0.25P(1 - 0.0004P).
(a) What is the long-term equilibrium population of carp in the lake?
(b) A census taken ten years ago found there were 1000 carp in the lake. Estimate the current population.
(c) Under a plan to join the lake to a nearby river, the fish will be able to leave the lake. A net loss of 10% of the carp each year is predicted, but the patterns of birth and death are not expected to change. Revise the differential equation to take this into account. Use the revised differential equation to predict the future development of the carp population.