Reading: Exponential Functions (part I)
Consider these two companies:
Graphs of data from A and B, with B fit to a curve.
This percent growth can be modeled with an exponential function.
Shana Calaway, Dale Hoffman, and David Lippman, Business Calculus, " 1.7: Exponential Functions," licensed under a CC-BY license.
- Company A has 100 stores, and expands by opening 50 new stores a year
- Company B has 100 stores, and expands by increasing the number of stores by 50% of their total each year.
- 100 stores, a 50% increase is 50 stores in that year.
- 1000 stores, a 50% increase is 500 stores in that year.
Years | Company A | Company B |
2 | 200 | 225 |
4 | 300 | 506 |
6 | 400 | 1139 |
8 | 500 | 2563 |
10 | 600 | 5767 |
Exponential Function
An exponential growth or decay function is a function that grows or shrinks at a constant percent growth rate. The equation can be written in the form f(x) = a(1 + r)x or f(x) = abx where b = 1 + r. Where- a is the initial or starting value of the function,
- r is the percent growth or decay rate, written as a decimal,
- b is the growth factor or growth multiplier. Since powers of negative numbers behave strangely, we limit b to positive values.
Shana Calaway, Dale Hoffman, and David Lippman, Business Calculus, " 1.7: Exponential Functions," licensed under a CC-BY license.