A common question about the exodus is how could the Jews have grown so fast. To look at just how fast it is I’m going to look at how fast their growth rate was compared to the fastest period of growth in the world, the Baby Boom. From 1950 to 2000 the world population rose from approximately 2.5 billion to 6 billion. This is a growth rate of approximately 2%. The Jews grew from 65 to 600000 in 210 years. This is a growth rate of around 4.5%. If you take the various midrashic accounts of the growth rate you get figures of 5.2% if 1/5 survived 6.4% if 1/50 survived and 7.6% if 1/500 survived. The non-midrashic growth rate is perhaps possible but not over that length of time. However it seems unlikely that these were the only people going down to Egypt. Jacob was rich and surely had some servants. It is entirely plausible that they had many servants who later were counted among the Jewish people. If they only had a Baby Boom growth rate they would have required 9300 servants a highly dubious number. However a 3% growth rate would have meant 1100 servants unlikely, but not impossible. Another strong possibility is that the Eiruv Rav made up a large number of that 600,000 for instance if there wer 530 servants and a 2.5% growth rate then the Eiruv Rav makes up around 5/6 of the population. The other problem is that around 1 in 20 males was a first born at the time of the census in the desert this strongly suggests 40 children in a family (Thanks Rachel for pointing this out to me) however if the Eiruv Rav made up 500,000 of the 600,000 and assuming that the Eiruv Rav had no firstborn sons you get closer to ten children a family with that method.
This whole approach is dubious at best and definitely a dochek, but it seems to be less of a dochek then the idea that women were popping out 6 kids at a time, the Jews were growing around 3 times the rate of the fastest documented growth in human history, and that each family had fourty children.
I would ne very interested in hearing any other approach which gets around these problems.