Does anybody know the exact formula for population growth?

[Rastaman]

The fastest population growth is achieved when you equalize the population over all colonies. Right?

Correct. For example, if you have 5 billion people and seed 3 worlds with 25 million each, after 50 years you have 10% less total population than seeding each with 250 million and 22% less than when seeding each with 1250 million. Time in cold sleep not considered.

If you have 10 colonies with 500 million each the advantage is 48%.

So a constant stream of colony ships to equalize the populations nets the largest growth. And likely a more lively empire, and more work.

[Brian Neumann]

One thing to think about with  faster growing population is that the percentage of the population generating wealth goes up with larger populations.  A small population has most of its people working in the agriculture and factories with only a small percentage working in the service sector.  A large population however has about 75% working in the service sector, and that is what generates money to spend.  A population of 400 million is about the cutoff for getting the 75% service sector.  A 100 million population has a service sector of 56% roughly.  Depending on how your population is split up this can have a big effect on your income and what you can actually spend it on

Brian

[Steve Walmsley]

One thing to think about with  faster growing population is that the percentage of the population generating wealth goes up with larger populations.  A small population has most of its people working in the agriculture and factories with only a small percentage working in the service sector.  A large population however has about 75% working in the service sector, and that is what generates money to spend.  A population of 400 million is about the cutoff for getting the 75% service sector.  A 100 million population has a service sector of 56% roughly.  Depending on how your population is split up this can have a big effect on your income and what you can actually spend it on

Brian

Wealth generation is based on the entire population. It isn't restricted to a particular sector.

Steve