wait, so you need to know figures in the sense of what is the year to year?

That's easy. Let's start at your base line: 200 people. Of the two hundred, we'll use the 4:1 ratio for non-workers: workers ratio. (Non-workers, in this case, means non-miners) So that gives us 40 workers.

According US Census Bureau, world historical population growth rate to be roughly 1.1%. (peaking at around 2% in the 60s) Let's round that down to 1% for easy calculations.

This is your base growth, and assumes that people are just popping out kids, with no additional people migrating over.

Now you need to consider several different factors that can change that number.

For ease of calculation, we're going to just assume that everything is rounded up.

For every spell level local cleric is capable of casting: +1% (I'm using this as a shorthand for the effects of technology)
A very um... "amorous" year: +1%
Food supply is well stocked this year: +1%
Significant Health and Safety improvement: +1%
Famine: -2% (can be higher if severe)
Disease: -2% (can be higher if disease is highly deadly, i.e. plague)


There are more, I'm sure. But as you can see, you can just add random +1% based the events you have in mind. Obviously, you can massage the numbers to make it work.

But even then, by natural growth, you won't get to 5000 from 200 in 10 years. That's a growth of 25 times. Compound growth indeed a powerful force, but not when your working with 5% growth per year. (With 5%, you'll hit 326 people in 10 years) No, to get to 5000, you need an average growth rate of about 38% per year to hit that target. However, towns can sprout up from the ground just like that in ten years. So how does it work? The answer is immigrants.

How many immigrants will come in? Well, that basically comes down to 2 things

1. is there a reason why people will want to come and stay
2. if there is, how well do people know about it

The first one will be need to be factored in by a number of things. How stable are the surrounding regions? how easy is it to live in your area compared to the surrounding regions? Is your area safer? (maybe because of the protection of your adventurers) Is there a lot of work available? Good school districts? What is it that makes your place so attractive? Is there a lot of trade? Do a lot of travelers need to pass through there just to go about their business? Is there a major artery road that passes by your town?

you can easily just give your town a +1% growth from immigration for that. (or you can calculate it separately) The best way to think about it is to think about how many people it is siphoning from nearby towns.

The second question will answer how FAR people will travel to come to your town. The more well known the place is, the more likely you'll get more people coming in. This can have a multiplier effect going on. So if your town is now incredibly famous country wide, it is entirely possible that you could be getting immigrants from all over the place to come to your town. In that case, you can think of it as having a multiplier effect. It can multiply the people that migrate to your town.

Just pull up excel and do a year by year growth calculation based on your events and you'll get pretty close.

Here's an example one

starting 200

year 1
good year for mine, attracting some people in nearby town: +1%
new cleric arrived, capable of casting 2nd level spells: +2%

growth rate this year: 4%.
new pop: 208

year 2
good year for mine, attract some people from surrounding towns: +3%
old cleric levels up, now capable of 3rd level: +3%
farmers have also arrived, bringing their stock and food production with them: +1

growth rate this year 7%
new pop: 223

and so on.