I am simply projecting population growth from 8 people over 50,100,200 years. In any case I also think that your estimate of 200 people after 100 years is extremely narrow. Thats at least 5 generations post flood, when the first generation yielded at least 16 grand sons.
Just for giggles, let's calculate the max population after the flood.
I dunno actually how many women where on board, but let's start the calculation with 1, and at the end we just multiply.
If we dump all other reasonable restriction on population growth (food, disease, etc...), there remains one important restriction: basic female biology. A woman can produce ~1 baby per year, and she can start having them when she's ~12. But since half of all children will be boys (pretty useless, since Noah can just impregnate all his daughters), a woman will only produce a girl every 2 years.
So if at year 0 after the flood, there is 1 fertile woman, she can produce a girl. In year 2, she will produce another girl. In year 4, 6, 8, 10, another. In year 12, the firstborn girl also get's a girl, so we have 2 new girls.. in year 14, we get 3 girls. In year 16, 4. In 18, 5. In 20, 6. In 22, 7. In year 24, the 2 girls born in year 12 also "start production", so the total number of new girls will be 9. In year 26, the 3 girls born in year 14 start production, so the total number of new girls is 12.
Or in c++, where we're taking 2 years as a single timestep:
Code:
int Noah(){
int births[51]={1};
int totalgirls[51]={1};
for(int i = 1; i<=50; i++){
births[i]=births[i-1]; //at least as many births as last period
if(i>6) births[i]+=births[i-6]; //adding the girls who were born 12 years ago
totalgirls[i] = totalgirls[i-1]+births[i];
cerr << endl << "Year " << 2*(i) << ", " << births[i] << " births, " << totalgirls[i] << " total.";
}
}
Which would make for a total of 466852 people after 100 years (although the fast majority of these would be underage; only 103598 girls are old enough to get kids at year 100. The number of adults (18+) are the number of births in the year 94: 62721.
Multiply by the number of adult woman on the ark (say.. 4?), and you'd get 250884 adult men by the time the tower of Babel is supposed to be build. That's the absolute maximum. If you add in real world factors (e.g., people dieing...), the population size will be drastically lower.
But then again.. Noah only had 16 grandsons? That would make it safe to say that he wasn't using this reproduction scheme =)
edit: yes, I'm bored.