Let y(t) be the number of thousands of mice that live on a farm; assume time t is measured in years_ The population of the mice grows at a yearly rate that is twenty times the number of mice. Express this as differential equation; At some point; the farmer brings C cats to the farm: The number of mice that the cats can eat in ayear is M(y) = € 2 + y thousand mice per year: Explain how this modifies the differential equation that you found in part a): Sketch a graph of the function Mly) for a single cat C = 1and explain its features by looking for instance; at the behavior of M(y) when y is small and when y is large. Suppose that C = 1. Find the equilibrium solutions and determine whether they are stable or unstable: Use this to explain the long-term behavior of the mice population depending on the initial population of the mice_ Suppose that C = 60. Find the equilibrium solutions and determine whether they are stable or unstable: Use this to explain the long-term behavior of the mice population depending on the initial population of the mice_ What is the smallest number of cats you would need to keep the mice population from growing arbitrarily large?'