Question

Let w be the number of worms in millions and r the number of robins in thousands living on an island. Suppose w and r satisfy the following differential equations: dw/dt = w - wr, dr/dt = -r wr. What is the question?

a) Find the equilibrium points of the system.
b) Determine the population growth rate of worms.
c) Analyze the impact of robins on worm population.
d) Solve the system of differential equations.

Answer 1

To find the equilibrium points of the system represented by the given differential equations, we set the rates of change of both variables equal to 0 and solve for w and r. The equilibrium points for w are when w = 0 or when r = 1. The equilibrium points for r are when r = 0 or when r = -w.

Step-by-step explanation:

The question asks us to determine the equilibrium points of the system represented by the given differential equations.

To find the equilibrium points, we need to set the rates of change of both variables, dw/dt and dr/dt, equal to 0 and solve for w and r.

By setting dw/dt = 0, we get w - wr = 0, which can be factored as w(1 - r) = 0. Therefore, the equilibrium points for w are when w = 0 or when r = 1.

Similarly, by setting dr/dt = 0, we get -r wr = 0, which can be factored as r(-r - w) = 0. Therefore, the equilibrium points for r are when r = 0 or when r = -w.