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1. Use excel to approximate the solution to the predator-prey model, where x(t) is the predator population and y(t) is the prey population: 
dx dt = —ax + bxy 
dy 
dt = cy — dxy x(0) = xo, Y(0) = Yo 
You should have cells for parameters a, b, c, d, as well as the initial condi-tions and time step h. 
2. Approximate the solution to the system with xo = 85, yo = 130, a = 0.1, b = 0.002, c = 0.2, d = 0.0025 and h = 1 up until t = 150 and plot the approximations with to on the horizontal and both x7, and yr, on the vertical axis. 
3. Consider the IVP below. 
dx 
dt= x + 4y dy dt   = 2 x + 3y x(0) = 1, y(0) = 1 
Verify that x(t) = e5t, and y(t) = e5t solves the IVP (plug in to system, and check initial conditions). 4. Use Euler's method to approximate the solution to the system above with h = 0.1. How far off is the approximation from x(1) and y(1)? Try it again with h = 0.01. What is the error now?