You have to account for the old folks dying, though, atpollard. (Unless you assume they *are* Adam and Eve!

) In <500 years, starting from a population of 1,000, it is possible to reach Pop 6 (maybe 7), with a generous population growth factor of 5%*. Hitting Pop 9 from 2 is a little bit tougher.
* For comparison, current pop growth factor in the US is around 2%, iirc. And, that includes immigration, and a replacement level of fecundity.
Either I am misunderstanding "population growth factor of 5%" or you have an arithmetic error.
5% growth = population x 1.05 per year
Over 500 years = 1.05^500 = pop x 39 billion
So 1000 people x 39 billion = 3.9 x 10^13 people = Pop 13
From another website, a 5% annual population growth = 72/5 = 14.4 year population doubling time.
Year 0 = 1000 people = Pop 3
Year 14 = 2000 people = Pop 3
Year 28 = 4000 people = Pop 3
Year 43 = 8000 people = Pop 3
Year 57 = 16 thousand = Pop 4
Year 72 = 32 thousand = Pop 4
Year 86 = 64 thousand = Pop 4
Year 100 = 128 thousand = Pop 5
Year 115 = 256 thousand = Pop 5
Year 129 = 512 thousand = Pop 5
Year 144 = 1 million = Pop 6
Year 158 = 2 million = Pop 6
Year 172 = 4 million = Pop 6
Year 187 = 8 million = Pop 6
Year 201 = 16 million = Pop 7
Year 216 = 32 million = Pop 7
Year 230 = 64 million = Pop 7
Year 244 = 128 million = Pop 8
Year 259 = 256 million = Pop 8
Year 273 = 512 million = Pop 8
Year 288= 1 billion = Pop 9
I suspect that for an interstellar TL civilization, planetary population levels are more of a cultural than biological choice.