While I agree that this approximation works well, your function for predicting the population (especially for humans) is rather generic. I am curious if you have thought about the potential of this argument had you extended this to be capable of holding multiple dynamic variables to more accurately predict populations? Either way the outcome would still produce a value that is much larger than the current population. I quite enjoyed the read, thank you for sharing! I reposted so more people can see it!
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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.
Well it is still done very well. If it would be okay with you, I would like to ask permission to be able to link this as a potential resource for when I see people make similar claims.
Of course! Thanks.