Identifying Exponential Behavior

We often want to know if something we are measuring is exhibiting exponential growth.

We do this by looking at the data.

Since our definition of exponential growth is that for a set interval on the x-axis, we multiply by a constant number on the y-axis.

We can then look at our graph or data for this behavior.

Ratios

For the following graph, we see that every time the number on the x-axis increases by one, we multiply by two on the y-axis. This is clear for x-values of 0, 1, 2, and 3 but it is also true for all other x-values.

For any graph, you can look at the ratio between points and see if it is constant, if it is, that graph is showing exponential growth.

Straight Line on a Log Scale

If we plot our data on a logarithmic scale, these ratios will be represented by equal distances and the data will lie on a straight line.

When data lie on a straight line when the x-axis is a linear scale and the y-axis is a log scale, the data is exponential.