27. Suppose that we have a population that not only grows logistically but alsorequires a minimum threshold population to survive. For example, the case ofthe North Pacific right whale, a species now very much on the endangered list. Ifthe population drops too low, whales might not be able to find suitable matesand the species will eventually go extinct. In other words, the population will dieout if it drops below a certain threshold. We can model this with the followingequation,dP= kdt(1-) (P- aN).(P – aN),(1.5.12)%3Dwhere P is the population of the whales at time t and N is the carrying capacity.The constants k and a are positive with a < 1.a. Find the equilibrium solutions of the this equation.b. Since equation (1.5.12) is autonomous, we can find a solution usingseparation of variables. Find this solution.c. Equation (1.5.12) is also a Ricatti equation (1.5.11). Since we know anequilibrium solution from part (1), we can use the method of the previousproblem to find a general solution to (1.5.12). Find the general solutionusing the fact that we have a Ricatti equation and show that your solutionagrees with the solution that you found in part (2)

Name: 27. Suppose that we have a population that not only grows logisticall
Uploaded: 2024-03-20T07:07:26.000Z
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Description: 27. Suppose that we have a population that not only grows logistically but alsorequires a minimum threshold population to survive. For example, the case ofthe North Pacific right whale, a species now very much on the endangered list. Ifthe populatio