For each predator-prey system, determine which of the variables, x or y, represents the prey population and which represents the predator population.

Is the growth of the prey restricted just by the predators or by other factors as well?

Do the predators feed only on the prey, or do they have additional food sources?

Explain.

[a]

dx/dt=-0.05x+ 0.0001xy

dy/dt=0.1y- 0.005xy

[Step 1] Identify what is give based on

Use the “predator-prey equations, or the Lotka-Volterra equations”

R represents prey. Wrepresents predator.

dy/dt=0.1y- 0.005yx ⇒ R=y=prey,k=0.1,a=0.005

dx/dt=-0.05x+ 0.0001xy ⇒ W=x=predator,r=0.05,b=0.0001

Since the equations model the Lotka-Volterra equations, they only affected by the prey and predators.

[b]

dx/dt=0.2x-0.0002x^2-0.006xy

dy/dt=-0.015y+0.00008xy

Since x is the prey, y is the predator and x^2 is involved, we see that the growth is also restricted by prey growth.