One would also have to take into account the factors that can slow population growth, especially infant mortality rates and disease epidemics. As late as the 1950s, infant mortality rates in the USA were around three percent. Globally today, it's still around 4-5%. In the distant past, it may have been as high as 50%. The Black Death of the mid-1300s may have wiped out more than a quarter of the world's population at the time, and the world population would take some 150 years to recover. And then there's the near-constant state of war the world seems to find itself in for as long as humans have been around.
A minor nitpick would be that we also have to assume a steady ratio of men-to-women to keep up an ideal rate of births. I have no idea if we've ever reached it, or how much that ratio fluctuates, but it could be a factor.