Chapter 9.1, Problem 45ES

(a) Suppose that a study of coho salmon suggests the population model

$p_{n+1}=\frac{2.08p_n}{1+0.00018p_n}$

Where $p_0=10,000$ is the number of salmon at the start of the study and $p_n$ is the population n years later. Based upon this model, what will the population of salmon be 10 years after the start of the study?

(b) Find a value of an initial population $p_0>0$ of coho salmon such that, with the recursion formula in part (a), the population remains fixed at $p_0$ from year to year.