This results in a separable ODE whose solution was used to generate the following table that shows how many turns it takes to populate a planet to various levels. It will start to break down when 1 turn corresponds less than a few hundred colonists. Scaling the above table would result in 433 turns.
Hull values are for the basic capacities.
These can be supplemented by using cargo pods. Here's the lisp code I used to generate raw data for the table. This table provides a visible justification for many of the population growth tips posted. Use the biggest colony ship you can build if you can afford the colonists. If you can't and you don't think you'll lose the world, wait until you can afford the colonists.