Here is a graph showing the luminescence of a glow-in-the-dark paint, measured in lumens, over a period of time, measured in hours. The luminescence of this glow-in-the-dark paint can be modeled by an exponential function.

Notice that the amounts are decreasing over time. The graph includes the point . This means that when the glow-in-the-dark paint started glowing, its glow measured 12 lumens. The point tells us the glow measured 6 lumens 1 hour later. Between 3 and 4 hours after the glow-in-the-dark paint began to glow, the luminescence fell below 1 lumen.

We can use the graph to find out what fraction of luminescence stays each hour. Notice that and . As each hour passes, the luminescence that stays is multiplied by a factor of .

If is the luminescence, in lumens, and is time, in hours, then this situation is modeled by the equation:

We can confirm that the data is changing exponentially because it is multiplied by the same value each time. When the growth factor is between 0 and 1, the quantity being multiplied decreases, the situation is sometimes called “exponential decay,” and the growth factor may be called a “decay factor.”