1. If population doubles in two generations, won't there be about 300 trillion of us (U.S.) in 20 generations or did I slip a decimal point
Twenty generations means the population will double 10 times. Taking the current pop=300 mil, this new pop will be 300 * 2^10
(where 2^10 means 2 to the power of 10 = 1024). Approximating 2^10 as 1000, yields a new population of about 300 billion.
2. it took approximately 3 million years to reach the present world congestion (at 6 billion estimated to be overpopulated from 5 to 20 times). At the foregoing rate of growth what would world population be in another 3 million years
Assume we start out with 2 humans 3 million years ago. (That's not quite right, but it was a small population and the actual number would not affect the results drastically.) Assume generations are 20 years. This means there are G=150,000 population increases (generations) in 3 million years. Of course, "G" is too big a number for the population to double. No population with finite resources can increase exponentially. Populations are limited by resources, predation, disease, and in the case of humans, war. We need to find the factor to use that will get us to 6 billion from 2 in 150K generations.
2*K^(150000) = 6000000000
Using logs, we find K=1.000145491
The number we want is N=2*K^(2*150000) = 1.8e19
(The e in this case doesn't denote the base of the natural logs, but engineering notation)
1.8 x 10^19 = 18 x 10^18 = 18 quintillion
However, this assumes the K is constant, which is a very bad assumption.
Large numbers revisitd
