Assuming once again that a generation is 20 years, we have 150,000 generations. The '2' denotes doubling, and the 300 mil is the starting population, we get:

N = 300e6 * 2^(150000) = 3e8 * 2^(10 * 15000)

The number is too big for my calculator, but we can play with it a little:

N = 3e8 * 1024^(15000)

I'm going to simplify, lose precision, and give you a lowball answer:

n = 3e8 * 1000^(15000) = 3e8 * (10^3)^(15000)
n = 3e8 * 10^(45000) = 3 * 10^45008

That's 3 followed by 45008 zeros - and this is a lowball answer.
Of course, the number is meaningless, as Pook pointed out. Just a sort of game, really.