2. There are initially 500 rabbits (x) and 200 foxes (y) on Old McDonald's Farm. Use Polymath to plot the number of foxes and rabbits as a function of time for

a period of up to 500 days. In addition, plot the number of foxes versus the number of rabbits. The predator/prey relationships are given by the following set of coupled ordinary differential equations: =k₁x-k₂x-y dx dt dy=k₂x-y-kay dt Where: Constant for growth of rabbits k₁ = 0.02 day-¹ Constant for death of rabbits k₂ = 0.00004 / (day x number of foxes) Constant for growth of foxes after eating rabbits k₂ = 0.0004 / (day x number of rabbits) Constant for death of foxes k4 = 0.04 day¹ Be sure to "Explain why..." and "Discuss which..." I want you to think a little about what your results mean. Not just what happens (ie. rabbits increase then decrease) but why (ie. do the rabbits starve to death or are they eaten by the foxes?) For help with Polymath, see the tutorials posted on Blackboard (available in the Documents section) What do your results look like for the case of k₂ = 0.00004/(day × number of rabbits) and trivel = 800 days? Again plot x and y versus time and y versus x.