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In haste I did not include the references where I provided what mathematicians consider sufficient proof, and I admit initiating the argument independently because it's so strong. But trust that I did not ignore "fundamental flaws" that have sometimes been presented with the argument.

Your equation is a model for UNLIMITED population growth thus it is meaningless in this context. Here is an example: they young earth crowd asserts that humans have been around for only about 6,000 years. For your equation to yield a current population of 6 billion, g works out to about .003644. Using this value, your equation yields the following results...

n	Year [AD]	p	Accepted Population (millions)
6000	2000	6,000,000,496
5900	1900	4,170,606,971	1600
5800	1800	2,898,993,511	1000
5700	1700	2,015,093,591	600
5600	1600	1,400,693,780	550
5500	1500	973,623,794	500
5400	1400	676,766,974	360
5300	1300	470,421,471	443
5200	1200	326,990,484	400
5100	1100	227,291,447	310
5000	1000	157,990,536	300
4900	900	109,819,396	226
4800	800	76,335,583	220
4700	700	53,060,948	207
4600	600	36,882,724	200
4500	500	25,637,222	195
4400	400	17,820,461	195
4300	300	12,387,022	220
4200	200	8,610,233
4100	100	5,984,982
4000	0	4,160,168
3500	-500	675,073
3000	-1000	109,545
2500	-1500	17,776
2000	-2000	2,884
1500	-2500	468
1000	-3000	76
500	-3500	12
0	-4000	2

As you can see, either your model is faulty or your model completely disproves the notion of a 6,000 year old human population.

According to your model, the total human population after 500 years would be 12 people. After 1000 years, 76 people. After 1500 years, 468 people.

Also notice how much your model differs from accepted population numbers in the last 500 years. Your model predicts a human population of 4 billion in 1900 while the accepted number is around 1.6 billion.