There are too many unknown variables such as catastrophes on the one hand or polygamy on the other. If it were (on average) a simple doubling, the present population could have been reached in a mere 30 generations.

But it's not necessary to go back that far, all you have to do is to look at the more recent rate of growth of say the past few hundred years and extrapolate that forward. But then obviously at some point, something has to give. No way is there ever going to be gazillions of people on this planet. Eventually there has to be either a slowing of the growth by social engineering to a point of equilibrium or catastrophic collapses by destruction of the environment and loss of capacity to provide the essentials of life to the whole population.