Mercurius
Legend
That is generally what I do (have done) however, in this case, I want to know what a semi-realistic number is since it is important in this specific case. I should clarify, the exact/specific/accurate "correct" number is not itself important, I just don't want the number of my choosing to be insanely off from what a formula might estimate (me saying a million when 10,000 is closer to the outcome of a formula, etc).
More specifically, I want to work out the starting (beginning) numbers so that they create my currently desired population, and so I have an idea of when such a thing needed to start (how long ago I should say) -- but this was just a long way of saying, "I need a population growth formula" hehe.
Again, weem, you can't really go wrong if you give a good context for why the city went from (A) to (B) population in (C) many years. A settlement of 200 people could, after 1,000 years, be extinct for 950 years, or it could still have a couple hundred people, or it could have turned into the Boswash Megalopolis of 55 million.
Of course if you are talking pre-industrial, it would be difficult to justify a city over a million people; AFAIK, our world only saw three pre-industrial cities of around that population, Beijing, Rome, and Constantinople/Byzantium/Istanbul. In Medieval Europe, over a hundred thousand was quite large.
But again, the main point: You can't go wrong in assigning a population figure, but you can go wrong in not matching it with a suitable context of climate, industry, migrations, etc. In other words, a settlement of 200 deep in the heart of an arid desert away from trade lines will never get that large. If it was located at a rich oasis on a major trade route, it could increase to a few thousand. And so on. I think this approach is key to attaining verisimilitude in campaign settings.