Immigration Model (a) In Examples 3 and 4 of Section 2.1

Chapter 3, Problem 3.1.72

(choose chapter or problem)

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 P(t) : ab as t : for P0 ab and for 0 P0 ab; as a consequence the equilibrium solution P ab 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 F(P) P(1 P) 0.3eP. Explain how this graph can be used to determine whether the number found in part (a) is an attractor. dP dt P(1 P) 0.3eP Q(0) 1 P(0) P(10) P(0) 10 0.035 Q(t) 1 P(t) P(t h) P(t) h 1 P dP dt 27069_03_ch03_p083-115.qxd 2/2/12 2:32 PM Page 103 . (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? 25