IMHO, a simple equation like I gave at first is adequate for game purposes. Yeah, I'm working on both right now. The units don't matter as long as you are consistent. How to find lambda for a given population, I don't recall. If you have two points on the curve, you can figure it backwards.
Population growth is an exponential curve.
Make sure r and n have the same time unit, if the rate of growth is in years then the time period needs to be in years. Plague, biowarfare, etc. This is very, very wrong. Population growth is the difference between the number of people born in a given year and the number of people who die. A growth rate of 0 would not necessarily mean that no children were born.