As time progresses the average age of the remnant increases as Nathan mentioned
This adds to the complexity of the analysis. I've tried several elementary functions on the remnant population curve such as, exponential, logarithmic, hyperbolic and quadratic. The hyperbolic functions gave the best fit so far. I'm not saying the curve is a standard hyperbola, but I think there are some hyperbolic tendencies in the curve. This population curve can broken down into separate functions that describe independant rates.
Most of these rates seem to be strictly time dependant, so the resulting equation that gives the remnant population at any time is probably a function of the sum of these rates
I think the best approach is to put the whole mess into a table format. I think that microsoft excel might be of use here. If I can get the result into this table format then one can see year by year the following data: Excel has math capabilities so I'll give it a try.
First there are two broad categories. The numbers of persons joining the remnant, lets call these the "INBOTS" . The number of persons leaving the remnant, lets call these the "OUTBOTS"
Now the OUTBOTS can be divided into more categories. The number of deaths. the number of those falling away(unfaithful) and the number who went to join the great crowd. The INBOTS don't seem to have any subcategories but we already know that they are wanabees or just plain mental. That is all I've done so far on the report, as far as getting "organized to accomplish our math"