Fishing for sardines: This is a continuation . If we take into account an annual fish harvest of F million tons of fish, then the equation of change for Pacific sardines becomes
a. Suppose that there are currently 1.8 million tons of Pacific sardines off the California coast and that you are in charge of the commercial fishing fleet. It is your goal to leave the Pacific population of sardines as you found it. That is, you wish to set the fishing level F so that the biomass of Pacific sardines remains stable. What value of F will accomplish this? (Hint: You want to choose F so that the current biomass level of 1.8 million tons is an equilibrium solution.)
b. For the remainder of this exercise, take the value of F to be 0.1 million tons per year. That is, assume the catch is 100,000 tons per year.
i. Make a graph of dN dt versus N , and use it to find the equilibrium solutions.
ii. For what values of N will the biomass be increasing? For what values will it be decreasing?
iii. On the same graph, sketch all equilibrium solutions and the graphs of N versus t for each of the initial populations N (0) = 0.3 million tons, N (0) = 1.0 million tons, and N (0) = 2.3 million tons.
iv. Explain in practical terms what the picture you made in part iii tells you. Include in your explanation the significance of the equilibrium solutions.