A while back, I ran across this argument from Answers in Genesis. In essence, they argue that world population doubles every 150 years. In other words, there are currently 6.5 billion people on Earth; if population doubles every 150 years, then there were 3.25 billion people 150 years ago, 1.625 billion 150 years before that. Trace it back, and you get an initial population of ~6 people round about the time that the Biblical flood was said to have occurred. ZOMG! This is exactly the number of breeding individuals that the Bible says survived the Flood! This would mean that the Flood story is true, and that the long time scale of human existence in evolutionary theory is impossible because at that rate of doubling, there would be more people than atoms in the universe!
I first found the argument referenced in this video, which did a pretty good job of demolishing the notion of a 150 year doubling--current population growth is the result of industrialization and modern medicine and agriculture being implemented in societies which previously had both high birth rates and death rates. Modernization reduces death rates before economic and other factors conspire to reduce birth rates, resulting in population boom--a pattern that played itself out in the first world, and is now being seen in the third world. The current rates of growth, however, are not indicative of all of human history, but only of modern agriculture and medicine combined with a still-high birthrate.
The Youtube video also referenced studies of population genetics, clear past examples of population decline (both local and global) and other useful arguments, but it missed a far simpler, mathematical argument. If population doubles every 150 years, then 150 years ago it was half of what it was now, and 150 years before that, it was half that, and so on. We could use this equation to determine the population at any given time:
Population = 6,500,000,000 / 2 ^ (# of years ago / 150)
This actually gives us a figure of 6 people 4500 years ago, which is the approximate date assigned to the Flood: the Bible says 8 survived, but only six were still of breeding age, so the math adds up. Rather conveniently, at that: it's almost as if they worked out beforehand what the rate of doubling would have to be to get from 6 to 6.5 billion in ~4500 years and then just used that number as their starting assumption.
But they apparently have no idea (or, more likely, assume that their audience has no idea) what the exponential growth curve would look like between the 6 and the 6.5 billion. Let's fill out some numbers and see where this takes us:
Year: Population according to AiG's formula:
2000 6,500,000,000
1850 3,250,000,000
1700 1,625,000,000
1550 812,500,000
1400 406,250,000
1250 203,125,000
1100 101,562,500
950 50,781,250
800 25,390,625
650 12,695,312
500 6,347,656
350 3,173,828
200 1,586,914
50 793,457
Riiiiiight. According to AiG's handy little formula, world population in AD 50 was just under 800,000. Meanwhile, in reality, Claudius' census in AD 47 revealed slightly less than 7 million Roman citizens--bearing in mind that citizens were a fraction of the population of the Roman empire, and that the Roman empire was only a fraction of the population of the world.
This humorous example is really all the proof we need that AiG's formula is innumerate at best and fraudulent at worst, but let's take it a step further. In the Bible, King David reigned over the united kingdom of Israel from 1003-970 BC, although these dates are approximate. 1000 BC is 3000 years ago--twenty doublings, as AiG would have it. This puts the world population at: 6,500,000,000 / 2 ^ (3000 / 150) = 6,200 people, give or take a few. However, King David took a census in which he counted 1,300,000 men of Israel and Judah who were capable of military service.
Sorry, AiG. The Bible says you're full of shit.
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