In relationships where the change is exponential, a quantity is repeatedly multiplied by the same amount. The multiplier is called the growth factor.

Suppose a population of cells starts at 500 and triples every day. The number of cells each day can be calculated as follows:

We can see that the number of cells () is changing exponentially, and that can be found by multiplying 500 by 3 as many times as the number of days () since the 500 cells were observed. The growth factor is 3. To model this situation, we can write this equation: .

The equation can be used to find the population on any day, including day 0, when the population was first measured. On day 0, the population is . Since , this is or 500.

Here is a graph of the daily cell population. The point on the graph means that on day 0, the population starts at 500.

Graph of an exponential function, origin O. Horizontal axis, number days, scale 0 to 4, by 1’s Vertical axis, cell population, scale 0 to 20,000, by 5,000’s. The function is discrete and has these points: (0 comma 500), (1 comma 1,500), (2 comma 4,500) and (3 comma 13,500).

Each point is 3 times higher on the graph than the previous point. is 3 times higher than , and is 3 times higher than .