Immigration Model (a) In Examples 3 and 4 of Section 2.1 we saw that any solution P(...

Immigration Model (a) In Examples 3 and 4 of Section 2.1 we saw that any solution P(t) of (4) possesses the asymptotic behavior as as a consequence the equilibrium solution P = a/b is called an attractor. Use a root-finding application of a CAS (or a graphic calculator) to approximate the equilibrium solution of the immigration model

(b) Use a graphing utility to graph the function Explain how this graph can be used to determine whether the number found in part (a) is an attractor.

(c) Use a numerical solver to compare the solution curves for the IVPs for P₀ = 0.2 and P₀ = 1.2 with the solution curves for the IVPs for P₀ = 0.2 and P₀ = 1.2. Superimpose all curves on the same coordinate axes but, if possible, use a different color for the curves of the second initial-value problem. Over a long period of time, what percentage increase does the immigration model predict in the population compared to the logistic model?

(reference example 3 and 4 in of section 2.1)