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 \(x_{0}\).
For what values of \(b\) will the series converge and diverge? What does the
series converge to?
