If the ratios of consecutive y-values are equal, then the data can be modeled by an exponential function. If the difference of consecutive y-values is constant, then the data can be modeled by a linear function.
Exponential function
Practice makes perfect
We want to check whether the given table represents a linear or an exponential function. If the ratios of consecutive y-values are equal, then the data represents an exponential function. If the difference of consecutive y-values is constant, then the data represents a linear function. Consider the given table.
x
- 1
0
1
2
3
y
0.25
1
4
16
64
Notice that the difference between each x-value is 1. Let's calculate the difference between consecutive y-values.
1-0.25&= 0.75, 4-1= 3,
16-4&= 12, 64-16= 48
We can see that the differences are not constant, so the data cannot be modeled by a linear function. Let's determine the ratios between consecutive y-values.
1/0.25&= 4, 4/1= 4, [0.6em]
16/4&= 4, 64/16= 4
Each ratio is equal to 4. Since the x-values are at regular intervals and the y-values differ by a positive common factor, the table represents an exponential function.
