Question to be answered in Mathematica A fixed population of birds discovers the

Question

Question to be answered in Mathematica

A fixed population of birds discovers the forest and feasts on the helpless flies every day, eating up to a maximum number of flies m. The flies' population model is now.

dn/dt=r n(1-n/k)-(m (n/a)^2)/(1+(n/a)^2) (2marks)

a) On one graph, plot the new predation term (2nd term on right hand side of equation (2)) between n = 0 and n = 100 with m = 5 and a = 1, 10, 20, 50. Remember to label your axes and include a descriptive legend, and make sure the whole axis is shown.

b) Solve equation (2) numerically between t = 0 and t = 10, using the initial condition n = 1 at t = 0 and the parameter values r = 0.1, k = 100, m = 5 and a = 20. Plot your solution on axes between n = 0 and n = 10, and with appropriate labels.

If the answer to this could please be made in the appropriate way to be put into Mathematica that would be fantastic.

Explanation / Answer

here it is...

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