5 Billion in a thousand years!
Now think how ridiculous millions of years sounds!
Are you seriously suggesting that there were 5billion people on the planet over 2,000 years before Jesus was born? I'd like to see how many people your 'accurate' model suggests there are today.
P(t) = 8e
0.02027*4000 = 8e
81.08
I make that out to be 1,300,000,000,000,000,000,000,000,000,000,000,000.
Do you think that's accurate?
If not, then we can conclude your model is flawed since it gives clearly absurd numbers.
The reason is clear: it assumes that humanity can and has always been able to grow exponentially. When you start looking at actual constraints of human population expansion and migration you find it is much more gradual with a lot more stagnation. The population tends towards its maximum at exponential rate, but as it hits that maximum mortality rates (disease, fighting over limited resources, high infant mortality etc) ensure it gets no further. Then a new piece of technology (like irrigation for example) comes along allowing for more resources to be gained increasing the maximum population a town or village can hold. Meanwhile, occasionally nomads would find a new place rich in potential and settle there.
Why would middle eastern people walk 5,000 miles within a year to find something that is in abundance closer to home? They wouldn't - it's unrealistic to think they would.
It would be interesting to see the actual proposed rate of expansion, a rough timeline with the number of people and the distance proposed that they go. The problems I foresee are spreading humanity far more thinly that practical too quickly, or not reaching places like China, India, Japan or America, quickly enough to account for what we know about history (actually they automatically fail on that alone, but it would be interesting to see how catastrophically they do fail.
So let's see: What was the approximate world population during the tower of Babel, how long did it take for them to spread across the world? What was the population of the world at that point?