You're totally right. I would never use this try to get an accurate function for population growth, and there are much more refined population growth models out there. The most important variables I can think of are changing rates of reproduction and changing lifespans. I tried to choose a time period after the biggest plagues and choose a very conservative lifespan, so that I could be fairly confident that I wasn't over-estimating...but there are other factors as well. Population growth rate likely increased a lot after the industrial revolution. I was motivated to take this approach by trying to think of a way that I could quickly refute the next person who made this claim to me using a napkin and a phone calculator.