Chapter 5.6, Problem 12E

C of these fish caught by fishing over the life span of the fish is given by the catch equation

$C=\frac{F}{M+F}{N}_0$

where F is the proportion of fish caught annually,

$M$ is the proportion of fish that die of natural causes annually, and $N_0$ is the original number of fish $F$ stocked in the lake. If we let $x$ denotes the ratio $\frac{F}{M}$, then the catch equation can be rewritten as

$C\left(x\right)=\frac{x}{1+x}{N}_0$

Assume that a lake is stocked with 1000 channel catfish

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

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

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

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