How long was it between the time of Noah / the flood and the building of the Tower of Babel?

Because there must have been massive population growth in that period of time to get from a population of 8 humans (some of them, like Noah) many centuries old (he was over 600 years old according to the Bible when he build the Ark) to a world population that could be scattered and punished with different languages so that they would be unable to interact.