Catch equation: If a lake is stocked with fish of the same age, then the total number C of these fish caught by fishing over the life span of the fish is given by the catch equation where F is the...

Catch equation: If a lake is stocked with fish of the same age, then the total number C of these fish caught by fishing over the life span of the fish is given by the catch equation

where F is the proportion of fish caught annually, M is the proportion of fish that die of natural causes annually, and N0 is the original number of fish stocked in the lake. Assume that a lake is stocked with 1000 channel catfish and that the natural mortality rate is M = 0.1 (this means that the annual mortality rate is 10%).

a. Write the catch equation for the lake stocked with channel catfish.

b. Assuming that F = 1 means that 100% of the fish are caught within 1 year, what might F = 2 mean?

c. What is the horizontal asymptote for the catch equation?

d. Explain what the horizontal asymptote means in terms of the original 1000 fish.

e. What is the vertical asymptote for the catch equation? Does the pole of the equation have any meaning in terms of the fish population?