Exponential growth is characterized by the speed of growth being proportional to the size of the thing that is growingthe bigger the thing gets, the faster it grows. This is another way of saying that the rate of growth is constant when the rate of growth is measured as the percentage increase over a fixed unit of time.

When something is growing exponentially, its size at any point in time is given by

A is the size of the thing at and δ is the continual growth rate.¹

In the real world many things grow exponentiallythings such as the number of bacteria in a petri dish, the amount of money in an account that earns compound interest, the size of my friend's Amway business, and of course the Mormon church. Invariably, exponential growth is only a temporary phenomenon. Sooner or later the bacteria run out of food, the money is withdrawn from the account, and the MLM network runs out of contacts. It's imaginable that the Mormon Church will grow at 50% per decade for the next 78 years and will reach 280 million in 2080, but if it were to then continue growing at that rate it would reach 16 billion in 2180 and 921 billion in 2280. At some point, circumstances always force exponential growth to stop.

When making long range forecasts of something that has been growing exponentially, the most important element of the forecast is estimating when the rate of growth will slow down. To do that, it is crucial to understand what internal properties cause it to grow exponentially, and what external environmental factors permit it to grow.

When exponential growth happens for an extended period of time, the internal driver of the growth is a mechanism where like creates like. In a savings account, money earns money. The new money that is earned is just as capable of producing more money as the money that created it. Thus the level of the account grows exponentially. When a bacterium in a petri dish splits, it creates two bacteria that have the exact same capacity to reproduce as the parent. Bacteria produce bacteria and the size of the colony grows exponentially.

On the other hand consider a hive of honeybees. In the beehive, the queen bee normally produces drones and workers, not queens. The drones and workers do not have the same capacity to reproduce as the queen. The population of the hive is limited to the number of bees that the queen can individually produce, so the number of bees in a hive would not grow exponentially.

The essential internal characteristic of exponential growth mechanisms is a process where like creates like. But what environmental factors are necessary for exponential growth to take place? The key environmental factor is a relative lack of competition. The reason why bacteria grow exponentially in a petri dish is because in that environment there is ample food and energy, no other organisms competing for the food and energy, and no predators preying on the bacteria.

The natural world is more complicated and competitive than the world in a petri dish. But exponential growth still occurs. This usually happens when something is filling a particular niche in the evolving ecosystem. A new plant that has a competitive advantage over the native plants might be introduced into a system. Its presence will grow exponentially, displacing native plants. But eventually the niche will be filled and new balance to the system reached. The alien plant will have displaced all of the plants that it was capable of displacing, and no longer be able to find more space with the properties that it needs to survive.

When something grows exponentially for an extended period of time you will always find these internal and external characteristics: It will be self-replicating producer multiplying in an environment where it has a competitive advantage.

With this understanding of what drives and permits exponential growth we will analyze the recent growth of the Mormon Church.

1.  Stark expresses growth rates on a per-decade basis. If d is the rate of growth per decade, that can be converted to the continual growth rate by the formula . So if the church grows at a rate of 50% per decade, that is a continual growth rate of .  (back)

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