(a) There are initially 500 rabbits (x) and 200 foxes (y) on Farmer Oat's property near Ria, Jofostan. Use Polymath or MATLAB to plot the concentration of foxes and rabbits as a function of time for a period of up to 500 days. The predator-prey relationships are given by the following set of cou- pled ordinary differential equations: dx =k,x-kx y dt dy = kxx.y-kay Constant for growth of rabbits k, = 0,02 day! Constant for death of rabbits kz = 0.00004/(day x no. of foxes) Constant for growth of foxes after eating rabbits kz = 0.0004/(day x no. of rabbits) Constant for death of foxes ki = 0.04 day! What do your results look like for the case of k, = 0.00004/(day x no. of rabbits) and t = 800 days? Also, plot the number of foxes versus the number of rabbits. Explain why the curves look the way they do. (b) Use Polymath or MATLAB to solve the following set of nonlinear algebraic equations xy-4y2+3x = 1 6y2-9xy = 5