I was looking at the current human population trend. As we know, the earth's population is rapidly approaching 7 billion. Only 50 years ago, the population was only 2 billion. Before this, the population rose at a fairly constant rate. If the trend was traced back to 4500 BC, then the population of the world would be nearly zero. If humans were around for even a million years, then the world would be truly overpopulated.
That's an oldie but not a goodie, from Morris in '74. The major problem, as has been pointed out, is that the population growth rate is not even close to constant and has almost always been much, much lower than it is now.
According to the Encyclopedia Britannica, the growth rate between 1900 and 2000 was 0.132% per year. Extrapolating that backwards yields 15,500 years to zero population, and is just as meaningless as your 4,500 years.
Estimates made by various organizations indicate much lower rates of population growth in the past. See
Historical Estimates of World Population.
We don't have good census counts from long ago, but we do have some data. For example, Augustine conducted a census of Rome in 28 BCE, and got 70 to 100 million people in the Roman Empire. How many people does your "model" predict were around at that time? Answer: world population of around 600,000. Therefore, there is something seriously wrong with your "model".
See
Population Size and Time of Creation or Flood and
Claim CB620 for more calculations and discussion.
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