After allowing their fish hatchery equilibrated at 25000 fish (without any harvesting), the owners[br]of fish.net have decided to allow harvesting based on the model [math]\frac{dP}{dt}=2P\left(1-\frac{P}{25}\right)-k[/math]. In this[br]model, P is the number of fish in thousands, and k is a harvesting rate measured in thousands[br]of fish per year. They initially allow a harvesting rate k = 12. If they allow fishing to continue[br]for a while at this rate, what does their model predict for the long term number of fish in the[br]lake?

The early years of fish harvesting went well, so they increased the harvesting rate by a modest[br]amount. They now allow harvesting rate corresponding to k = 13. What does this model predict[br]will be the long term result of this fishing practice?

The owners of fish.net panicked when their fish population reached P = 5 and decided to return[br]to their original business model with k = 12. Will the fish population return to the levels you[br]described in problem 1a? Why or why not?[br]