_ ' There is a very famous model called the Lotka-Volterra predator-prey module that we will come up with here. (Try it without looking it up!) If we take $03) as the number of prey at time t and y(t) as the number of predators at time t, then we have the following assumptions on prey: - Left alone, the birth rate of the prey is proportional to the population size of the prey. . The prey are more easily killed if there are many prey and/or many predators, so the number of prey killed is jointly proportional to the two populations (see problem 4 - proportional to the number of encounters between them). We have the following assumptions on predators: - The predator population grows proportionally to the number of encounters between predator and prey (that is, jointly proportional since predators have evolved to reproduce when food is plentiful but not as much when food is scarce.) . Predators can be very territorial, so the death/exit rate is proportional to the number of predators. (That is, the predators are more likely to be killed or driven off as the predator population increases). a. What is the system of differential equations (aka your model)? If it helps, flrst draw a schematic