Chapter 5, Problem 401RE

The following problems consider a simple population model of the housefly, which can be exhibited by the recursive formula $x_{n+1}=b{x}_n$. where $x_n$is the

population of houseflies at generation n. and b is the average number of offspring per housefly who survive to the next generation. Assume a starting population x₀.

401. Find $\underset{n\to \infty }{\lim }{x}_n$ if b > 1, b < 1, and b=1.