Exercise 28

The growth of a population of rabbits with unlimited resources and space can be modeled by the exponential growth equation, $dP/dt = kP$.

1. Write a differential equation to model a population of rabbits with unlimited resources, where hunting is allowed at a constant rate $\alpha$.

2. Write a differential equation to model a population of rabbits with unlimited resources, where hunting is allowed at a rate proportional to the population of rabbits.

3. Write a differential equation to model a population of rabbits with limited resources, where hunting is allowed at a constant rate $\alpha$.

4. Write a differential equation to model a population of rabbits with limited resources, where hunting is allowed at a rate proportional to the population of rabbits.