Does anyone know the population growth formula?

Unless I've missed something in a recent patch, the base population growth is a constant defined in GalCiv3GlobalDefs.XML. Look for the GlobalColonyMod with an EffectType of Growth.

The formula for the difference in a planet's population between this turn and next turn is r * (1 + approval_mod + other_bonuses), where r is the base population growth defined in GalCiv3GlobalDefs, approval_mod is a number between -0.25 and +0.25 which can be computed using the planet's current approval rating expressed as a decimal and the curve defined by a set of points in GalCiv3GlobalDefs (the points can be found by searching for ApprovalToGrowthCurve; I'm pretty sure the game just uses linear interpolation between the points to get the value of the modifier), and other_bonuses is the sum of the bonuses from structures built upon the planet (e.g. Colonial Hospitals) and empire-wide bonuses such as those from Artocarpus Viriles (5% per AV) and technologies.

Thank you joeball123!  That's what I thought, and just so everyone knows, the value is Growth in GalCiv3GlobalDefs.xml is as follows:

<GlobalColonyMods>
<EffectType>Growth</EffectType>
<Target>
<TargetType>Colony</TargetType>
</Target>
<BonusType>Flat</BonusType>
<Value>0.05</Value>
</GlobalColonyMods>

The default value is 0.2 and I turned it down to 0.05.

Turns out that the main source of my confusion is that this is the value I was editing in my mod but the effect wasn't taking within the game.  I have mods enabled and the other changes are taking effect.  I had to make the change within the game directory in steamapps.  This doesn't seem right as it will be overridden during updates.  Is GalCiv3GlobalDef.xml not editable within a mod?

Within the mod folder the path to the xml file is as follows:

~/data/Game/GalCiv3GlobalDefs.xml

Thanks,

Joe