[thrash]

If you sidestep environment and resource constraints, the biggest limiting factor on colony growth is infrastructure development. This, in turn, is driven by the tech level you want the colonies to maintain on their own: TL5 is easy (with the right starter package and skill set); TL9^ will take work.

Infrastructure can be created locally, by existing colonists, or imported. The main difference is that local infrastructure can benefit from exponential growth, while imported infrastructure requires resources (ships, mostly) that are likely to have a cap. The balance between the two shifts from all imports in the establishment phase to all local by the time the colony is fully mature and sending out daughter colonies of its own.

Eric's figures on growth rates are pretty good. I suggest you look at how much shipping you want to have available (which may grow over time), how much imported infrastructure each new colonist needs (in tons, on average) to be productive, and therefore how many colonists you can add per year over the organic growth rate.

Your initial population will look like an investment curve with interest plus regular payments -- much faster than just based on interest alone. Once the local population and infrastructure increases exceed the imports, you can quit worrying about imports.

Remember that each world has a saturation population level, based on habitability, resources, and tech level. As you reach that point, the growth curve should level out and then stabilize around that value. This is a reasonable point for some worlds to start sending out daughter colonies.

In my worldbuilding, I usually anticipate that this saturation point is reached in about 400 years of uninterrupted (by war, collapse, etc.) colonization.