- Df 0 45 1 2 17 A Suppose That A Population Of Fish F T In Thousands Satisfies The Logistic Growth Model Given By 1 (110.42 KiB) Viewed 19 times
this is all one problem
df 0.45(1-2) 17. a. Suppose that a population of fish, F(t) (in thousands), satisfies the logistic growth model given by F = F dt 200 where t is in years. Solve this differential equation with F(0) = 50. b. Find all equilibria for this model. Sketch a graph of the right hand side of the model, then draw the phase portrait on the F-axis. What is the stability of each of the equilibria? Determine the carrying capacity for this population of fish. c. Assume that fishing is allowed and that 15,000 fish are harvested annually. The model becomes dF F = 0.4 F dt Find all equilibria for this model. Sketch a graph of the right hand side of the model, then draw the phase portrait on the F-axis. What is the stability of each of the equilibria? Determine the carrying capacity for this population of fish. What is the threshold number of fish needed to avoid extinction? F(-X) - 15. - .