I don't understand why you have 38k number there, it's nonsense. Growth rate is calculated per year, not 30 years.
because they need 30 years to mature and reproduce AKA grow in number - NOT 1 year.
But if you using a 0.02 growth rate, that's 2% annually, not 2% every generation. The mistake you're making is you're actually using a 0.00066 annual growth rate, this is why the number you're getting (38,190 people) after 2,000 "annuals" is so incredible small.
0.02 divide by 30 give you 0.00066.
Even if each generation is thirty years, statistically the birth rate for a population group is calculated over the total time period.
If the romulans were breeding like tribbles, then they could reach ~1-10 billions in 2000 years.
In one of my previous post I said:
If we started with 10,000 people, and each couple in each generation produced an average of 3 children who in turn reproduced, the population of the Empire could be up to 110 billion people.
Now, I did stipulate three children surviving
to reproduce another surviving three children. Not three children born. This statement takes into account children and adults who don't survive to reproduce the average number. So, at that rate of population growth, you don't get "~1 - 10 billion," you get 110 billion people in the current population after two thousand years. This already takes into account illnesses, accidents, warfare and all other causes of "not reproducing the average number