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.
Linear 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
- 3
0
3
6
9
y
10
1
- 8
- 17
- 26
Notice that the difference between each x-value is 3. Let's calculate the ratios between consecutive y-values.
1/10&= 1/10, - 8/1= - 8 [0.8em]
- 17/- 8&= 17/8, - 26/- 17= 26/17
We can see that the ratios are not equal to each other, so the data cannot be modeled by an exponential function. Let's calculate the difference between consecutive y-values.
1-10&= - 9, - 8 - 1= - 9 [0.8em]
- 17-(- 8)&= - 9 - 26-(- 17)= - 9
Each difference is equal to - 9. Since the x-values are at regular intervals and the y-values differ by a constant, the table represents a linear function.
