You use an exponential model when you notice that the coordinates of the points are either increasing or decreasing in value very quickly. Remember, each set of points has its own unique best model.

Because there’s an infinite amount of ways to create a collection of points that can be modeled as an exponential expression, there’s an infinite number of graphs that fit the expression below. The only difference between these graphs is the values of the coefficients $a$ and $b$.

Theory

Exponential growth means that there is an increase by a fixed percentage over each period. Exponential decline means that a decrease by a fixed percentage over each period.

A typical example of when it’s appropriate to use an exponential model is when you’re modeling population growth. This applies to people within a specific geographical area, animal populations, or the number of bacteria in a Petri dish.

Another situation where an exponential model fits well is when you have an increase in value, or a loss of value. This can be money in an interest-bearing bank account, or the value of a car.