Question: The predator-prey model for the number of robins, r, in thousands, and the number of worms, w, in millions, was for some positive constants a, b, c, k:
(dw/dt) = aw - cwr and (dr/dt) = -br + kwr
(a) Find the equilibrium points of this system of equations.
(b) An insecticide is applied to the ground, causing a decline in the number of worms proportional to their population. What effect does this have on the equilibrium point? Interpret this in terms of the equilibrium population of worms and robins.