Assume that a city has a feral cat population of 2,000 cats and that the cats have a net growth rate of 0.4. In this phase of the project, we study various ways to deal with this cat population. We assume throughout the section that population growth is proportional to the current population.
Scenario 1: In this scenario, assume no action is taken to limit the growth of the cat population. Derive the differential equation governing this scenario and solve then solve that differential equation.
Scenario 2: The Trap-Kill method of population control consists of laying out R traps and killing any cat caught by the trap. For this method, assume each trap catches a cat during each time step, and assume that the cats breed before they are caught. Derive and solve the differential equation for this method.
Scenario 3: The Trap-Spay/Neuter-Return method consists of using traps as before, but instead of killing the cat, the cat is is Spayed/Neutered and then returned to the city. In addition to the assumption used above, assume that no cat is caught by the traps twice. Again, derive and solve the differential equation for this method.