Thank goodness for the internet! I found a website that does all the 
nasty calculation of exponential regression for me. Army sizes in 
Celandra can be approximately calculated using the formula:

y = 16.2645x^0.518867

or, if you're in a hurry and just want a quick'n'dirty number,

y = 16 * squareroot(x)

where x is the population of the country and y is the nominal army size. 
The equation doesn't *quite* fit for x > 200,000,000 or so, but for most 
  MidSea countries, it should work adequately.

Andrew

Andrew Janssen wrote:
> I'm trying to work out some sort of equation, such that you can plug 
> your population number into it and get your nominal army size out. 
> Unfortunately for me, the military% changes nonlinearly, and it's been 
> seven years since I took calculus. I can tell from plotting the existing 
> points that any such equation would involve exponential functions, but 
> like I said, my math is really rusty.
> 
> Anyone out there with decent math skills? I can probably figure it out 
> if I bang my head against it often enough, but I'd like to spare myself 
> as much pain as possible.
> 
> Andrew
> 
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