If the ratios of consecutive y-values are equal, then the table represents an exponential function. If the difference of consecutive y-values is constant, then the table represents a linear function.
Exponential function
Practice makes perfect
We will determine whether the table represents a linear or an exponential function. If the ratios of consecutive y-values are equal, then the table represents an exponential function. If the difference of consecutive y-values is constant, then the table represents a linear function. Consider the given table.
x
0
1
2
3
y
8
4
2
1
Let's calculate the difference between consecutive y-values.
4-8= - 4, 2-4= - 2, 1-2= - 1
We can see that the differences are not constant, so the table does not represent a linear function. Let's determine the ratios of the consecutive y-values.
4/8= 1/2, 2/4= 1/2, 1/2= 1/2
Each ratio is equal to 12, so the table represents an exponential function.
