I have been looking all over for a formula or program to determine a maximum possible human population size within a $106$ year span. This specifically is in response the the claim by the Creationist organization "Answers in Genesis" that The Tower of Babel dispersion of humans into different languages and races occurred 106 years after the end of the great flood.
In order to be as generous as possible, I would like to make a few basic assumptions to ensure this is an unreasonably high estimate by any and all accounts.
The initial population is $3$ breeding pairs, and we assume that they give birth within the first year after the flood. For ease of math, we will say that all births are singletons, and each woman above the age of $13$ gives birth every $2$ years for $20$ years, for a total of $10$ offspring. Sex is split evenly between male and female, rounding toward female. Assume zero deaths or infertility.
So initial population ($P$) is $3$ females at $t=0$. At $t=1$ until $t=14$, population of fertile women still $= 3$. At $t=15$, population of fertile females $=5$...
I would like to know for $t=106$: the total global population, the total fertile female population, and if possible, the percentage of the total population above the age $13$.
I have no idea how to figure these things out. Can anybody help me?
Here is a very simple C-program: http://ideone.com/GKvh6J. Its result (see the "stdout" section):