How can I determine the number of years it would take to reach my desired population growth?

Impossible to tell based on these parameters. They're actually the least important ones.

the important ones are:
- technology level of the people
- friendlyness of the habitat
- predators

Just look at the increase in human population on earth. The growth is very exponatial simply because as our technology has become better we live longer, can feed more people, can heal injuries better and so on. We can survive easier in harsher climates and we have less and less to fear of predators.

if you're starting from cavemen, then it took humans something like 100.000 years to spread across the globe. Though again, that spread wasn't uniform. It took us 50k years to get out of Africa and another 50k years to spread everywhere. So for something 25 times larger it might take anything from 25 times longer to only twice as long.

Once humans settle down then all bets are off. In cosmic terms we conquered the earth in the blink of an eye, going from a few million to 7 billion in only 3000 years or so. Once they're spread everywhere, then I wouldn't expect this speed to change simply because it's down to how fast can a single group of people grow locally.

So if you want an estimate then I'd go with 175.000 years, give or take 100.000 years.

 

uhhg...

starting population x 1.02 per year might be something to start with...or if they have especially large families, maybe starting population x 1.05 per year...

 

There is no definitive answer to this. It depends on the level of civilisation, the nature of the environment, social conventions and other factors such as disease etc. It is like asking 'how long is a piece of string?'

The area that became the Roman world saw growth of 0.1% per year from 1200 BCE to 200 CE. That was pretty fast growth for the ancient/medieval world. From about 200 CE to 1800 CE, the European half of the empire only saw about 0.06 to 0.07 percent annual growth. Populations in places like Africa and parts of Asia saw no significant growth at all during the middle ages.

Of course the average hides many ups and downs (the Black Death reduced European populations by 1/3 to 1/2 in a few short years for example).

In more modern times population growth accelerated far more rapidly.

 

I am questioning if this would really be an issue. Seems like something planners want to know, but never turns out to be actual anyway.

Population will rise and fall for many reasons, one of which will include the perception of many that the place can or cannot sustain more population. And as population rises, so would the ability of these to live off world.

If you need an exact number, take the number of people currently, apply a growth rate and start doing the math. Would that number be actual in a real world sense...probably not.