How do we know how fast global human populations grew in the past?
You could create a realistic population growth model and work it out. The best known creationist human population growth models have been very flawed, committing the "Bunny Blunder" (ie, applying their model to the world population of rabbits, then that population would have resulted from 2 bunnies about 100 years ago).
Back in 1991, I posted an article on CompuServe that examines Dr. Henry Morris' (PhD Hydraulic Engineering) human population model as he had presented it in a few places -- he continued to develop it over time -- , as well as actual population growth models that address the problems of Morris' over-simplistic "pure-birth" model. I've re-posted it at http://cre-ev.dwise1.net/bunny.html.
One of the problems that had been pointed out about his model and which your model will likewise have to deal with is that when we apply it to find the world population in the ancient past, we come up far too short to account for the massive construction of that time. From my article:
quote:In his article, "Creationists, Population Growth, Bunnies, and the Great Pyramid," David H. Milne points out that since Morris' population model is predictive, then we should be able to use it to determine the world human population at any time in human history. Therefore, it reveals some interesting facts about human history.
According to Morris' model, in 2500 BCE, the world population was 750 people, so there were only about 150 to 200 able-bodied males, all concentrated in Egypt, available to hew and haul the 2.3 million limestone blocks ranging in weight from 2 to 50 tons to build the Great Pyramid of Cheops. During the preceding 200 years, even fewer men built six neighboring pyramids and many other structures. Things were even more hectic back between 3800 BCE and 3600 BCE when the total world population of 10 - 20 people, including women and children, rushed madly back and forth between Crete and the Indus River Valley building and abandoning enough fortified cities and massive irrigation systems to have housed and fed millions. My father was right; we HAVE gotten soft!
Now, Morris' model was based on Adam and Eve and not on the survivors of Noah's Flood, which means that your model will have to deal with even less time to build up the world population to a point where they could have built what they had left behind and much more.