How long has Humanity been on Planet Earth?

[Pat Mustard]

A generic question. How long does the population of humanity take to increase from 2 (or more than 2) to the current 8 billion (give or take)?

Population Doubling Time is a well known concept. It takes around 200 to 300 years at most for a population to double. But if that is true, since 2^10=1024=1000 (approx.), then it takes only 2000 to 3000 years for a population to increase by a factor of 1000. Next, since the population is only in the billions and not the trillions, there have been only 3 such increases [(10^3)^3] in all of human history. But that leads to a far younger date for the origin of the first human couple (or couples) than most evolution-supporting Atheists would agree with. Stated differently, if humanity began around 100,000 B.C. but yet doubled around 200 to 300 years, and increased by 1000 every 3000 years or so, the population would be >10^30, i.e. Millions of Trillions of Trillions, not just 8 BN. How do we resolve this dilemma/paradox, from within the evolutionary paradigm?

Thoughts and comments welcome.

Knowing I'm speaking to a probable sockpuppet here (no matter, they're banned), but has the OP not realised that it's only in the last few hundred years humanity as a species has developed enough to escape the clutches of its predators (large carnivores, diseases) and to be able to explode in population.