How do the consecutive terms relate to each other?
Exponential
Practice makes perfect
We want to identify which kind of model best describes the data: linear, quadratic or exponential. To do so we will calculate the difference and ratio between consecutive terms.
x
-1
0
1
2
3
y
3
6
12
24
48
Let's begin with calculating the first differences.
The first differences are not all equal. Therefore, the table of values does not represent a linear function. Let's find the second differences and compare them.
The second differences are not all equal. Therefore, the table of values does not represent a quadratic function.
The ratios of successive y-values are equal. Therefore, the table of values can be modeled by an exponential function.
