We said in equation (1.1) that when something is continuously growing at an exponential rate it can be represented by

In this formula, the variable can be thought of as the force of growthas long as is a constant then the size of the church will grow exponentially, but the larger , the faster the exponential growth.

The constant can be calculated by the formula

Over a 1-year period, the growth of the church can be broken down into 3 components: growth due to convert baptisms is denoted b, growth due to children of record being baptized is denoted c, and decrements due to people leaving the church through death, excommunication, or voluntary name removal are denoted d. Thus the number of members at time is equal to

Substituting (4.2) into (4.1) results in the formula

Which is equivalent to

So for the church to grow at a constant exponential rate, the following must be constant for all years:

That is nothing other than the annual growth rate, broken down into 3 components.

But what if the value of changes from year to year, or for that matter, from moment to moment? Let be the value of at any given point in time. Assuming that the function is continuous, formula (1.1) can be generalized as

If you have a question or would like to discuss these topics, I suggest that you go to a Mormon-related bulletin board. If you'd like to <i>contact me</i> with comments or feedback, you may send an email to analytics@lds4u.com.CompanyEmail