There are initially 500 rabbits (x) and 200 foxes (y) on Far

There are initially 500 rabbits (x) and 200 foxes (y) on Farmer Oat’s property. 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 coupled ordinary differential equations:dx /dt=k1 ·x−k2 ·x·ydy /dt=k3 ·x·y−k4 ·y Parameters are as follows:Constant for growth of rabbits k1 = 0.02 day−1Constant for death of rabbits k2 = 0.00004 (day x no. of foxes)−1Constant for growth of foxes after eating rabbits k3 = 0.0004 (day x no. of rabbits)−1 Constant for death of foxes k4 = 0.04 day−1Additionally:• Plot the number of foxes vs. the number of rabbits.• Solve the case where k3 = 0.00004 over a period of 800 days. • Interpret each of your plotsUse Polymath or MATLAB to solve the following set of nonlinear algebraic equations for x and y.x^3y − 4y^2 + 3x = 1 6y^2 − 9xy = 5

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