There is no particularly logical reason to posit a constant or even continuous growth rate for the human population.
Even in historical times we know of periods during which the population in various areas stagnated or even declined sharply.
In the course of about a century the human population off the world dropped by about 10% due to Mongol massacres.
China has a repeated cycle over the last 3000 years of one dynasty falling apart,partially due to population reaching its limits with available resources. The resultant chaos often lasted for decades or even a century or two. When the next dynasty finally got control, the population was often 25% to 50% of what it had been under the previous dynasty. Population starts to built in the peace created by the new dynasty... Rinse and repeat.
Population under the Roman Empire was a large multiple of that supported during the Dark Ages.
The human population of the Americas dropped by something liked 85% to 95% during the 1500s as a result of the introduction of Afro-Eurasian diseases.
The historical growth rates I use, already reflect that, it’s got the plague, the dark ages, the wars, etc built in. I just don’t buy that mankind was around 100,000 years and maintained small numbers for the first 95,000.
Just look at the documented growth rates of the last 5000 years. Or any 1000 years and you’ll see what I mean.
And some archeological finds would have us believe that modern humans were around much longer than that.