Q:

How can I find the total number of rabbits if they reproduce at a constant rate?

The problem is as follows:

Roger adopts two female rabbits and two male rabbits. Three months
  later each female rabbit gives birth three female rabbits and three
  male rabbits. Assuming that if the same happens every three months.
  How many rabbits maximum would Roger have after a year from the
  adoption of his pets?.

The alternatives given in my book are as follows:
$\begin{array}{ll}
1.&\textrm{486 rabbits}\\
2.&\textrm{2048 rabbits}\\
3.&\textrm{512 rabbits}\\
4.&\textrm{1024 rabbits}\\
\end{array}$
How exactly can I find the number of rabbits in this situation?. I don't know if the fibonacci sequence applies in this situation. Or can this be solved using a just ordinary equation?. What sort of rationale should be used here?.
Since I'm slow learner. Can someone explain me this step by step? please.

A:

As the number of rabbits added is thrice that of the original, the population of rabbits is quadrupled every 3 months. As such the growth can be modelled by $4^{(n/3) + 1}$, where n is the time in months after the first adoption.
This can also be done iteratively as such:

0 months:                  2F, 2M
      3 months:                2F, 2M + 2(3F + 3M) = 8F, 8M
      6 months:                8F, 8M + 8(3F + 3M) = 32F + 32M
      9 months:                32F + 32M + 32(3F + 3M) = 128F + 128M
      12 months(1 year):       128F + 128M + 128(3F + 3M) = 512F + 512M  

... Where F represents the female rabbits and M represents the male rabbits.
There should be 1024 rabbits after a year, unless I'm missing something crucial.

