Question: If 2 rabbits were fertile two months after they were born and they had two rabbits every month (when fertile) , how many rabbits would there be after twenty months if all the other rabbits they had were the same?

Laurence Perreault Levasseur answered on 20 Jun 2014:

hahaha! that sounds like you are trying to make us solve your maths homework questions, sonyandmary 😉
The answer is that the number of rabbits grow exponentially with time.
To solve this problem, you can write the rate of change of the number of rabbits for every month. It’s equal to the number of rabbits there were two months ago (since rabbits can reproduce on month 2 of their life). So if x is the number of rabbits, and t is the month,
then dx(t)/dt=x(t-2)
You can solve this differential equation pretty easily numerically (I think :P, but I’m not sure in what year you are…). To solve it, don’t forget to impose the initial conditions! You can fix them imposing that initially, so at t=0 and t=1 (at first and for the first month, before the couple can reproduce), there are 2 rabbits, so x(t=0)=x(t=1)=2.
Here is also a graph that shows how the population of rabbits evolves:
https://www.dropbox.com/s/r96qd7erb35ebiv/rabbits.pdf
I hope this helps 🙂

Edit: I corrected the differential equation to account for the fact that the rabbits take 2 months to mature! So sorry I had misread the question at first and thought they reproduced after just one month!!