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
Let's 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
y
1
6
2
12
3
24
4
48
Let's calculate the difference between consecutive y-values.
12-6= 6, 24 -12= 12, 48-24= 24
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.
12/6= 2, 24/12= 2, 48/24= 2
Each ratio is equal to 2, so the table represents an exponential function.
