A pet store plans to start selling mutant fish. They will have two types available: one-eyed and three-eyed fish. Denote the population of one-eyed fish by x(t), and the population of three-eyed fish by y(t). After placing the two fish species in the same tank, they realize the fish fight each other. They will however, receive additional fish every week. The store manager, who is an expert in mathematical modeling, has concluded that the weekly changes in the two populations are described by the following system:

x'(t) = 3.8x - 2.4 y + 13 L'(t) = -2.4x + 0.2y + 1

1. Find the equilibrium solution. (Get the algebra right or the problem will break. The coordinates of the equilibrium solution should be integers.)

2. Classify the equilibrium according to type and stability. (Again, careful with the algebra. The eigenvalues should be integers.)

3. What will happen to the two mutant fish populations if the store starts with 5 three-eyed fish and no one-eyed fish?

4. What will happen to the two mutant fish populations if the stores starts with 4 three-eyed fish and no one-eyed fish?