# Exponential Growth problem with a twist.

I've been searching for a solution to the following problem(s) for quite some time. The answer is uncomplicated in nature, but I haven't been able to get far without bruteforcing it. Can anyone assist me? Here's the problem:

1. A female rabbit reaches sexual maturity between 3 and 6 months old. The litter size is between 4 and 12 rabbits. The gestationn period is between 28 and 31 days. Create a model to predict rabbit population after 5 years if the initial population contains 1 female and 1 male. Assume 0 mortality."

2. Falcons are introduced into the ecosystem one year after the male and female rabbits began producing. Falcons consume 15% of the rabbit population every month. Create a model of this after 4 years.

As I said, I've bruteforced it (actually written down the months, adding the doubling of the years, etc.) It feels like a recursive sequence wrapped up in a nasty exponential growth pattern; it doesn't "feel" like the regular exponential growth problems I've dealt with before. I'd appreciate it if anyone can assist me! Thanks.

• We can also assume that the litter size is 12, and that 6 males and 6 females are produced in every litter size. We can also assume it takes 6 months for sexual maturity. Maybe that will simplify things more. – john doe May 20 '18 at 21:42