What is an exponential function?
An exponential function is a function in which the y-values have equal ratios while in a linear function the y-values have equal differences. For example in a linear function the values would look something like this, because each y-value is 1 more than the value before it:
An exponential function is a function in which the y-values have equal ratios while in a linear function the y-values have equal differences. For example in a linear function the values would look something like this, because each y-value is 1 more than the value before it:
In an exponential function, the values would look something like this, because each y-value is 3 times more than the value before it:
How to use exponential functions:
A exponential function is where the independent variable is the exponent and the general form of an exponential form follows this formula, where b is a constant and x is the independent variable:
The following graph is an example of an exponential growth function as the graph increases rapidly:
The following graph is an example of an exponential decay function as the graph decreases rapidly (getting smaller as x increases):
Sample Math Problems
1. What kind of function best models this relationship?
a) Linear
b) Exponential
b) Exponential
Solution: Option A – Linear. The difference in y values is the same (each time it increases by 2)
2. What kind of function best models this relationship?
- XValues
- YValues
- 0
- 3
- 2
- 6
- 4
- 12
