How do the consecutive terms relate to each other?
Type of Function: Exponential Function: y=3* 4^x
Practice makes perfect
Finding the Model
We want to tell whether the table of values represents a linear, exponential, or quadratic function. To do so, we will analyze how the consecutive terms are related to each other.
x
-1
0
1
2
3
y
0.75
3
12
48
192
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. Let's find the ratios of the y-values and compare them.
The ratios of successive y-values are equal. Therefore, the table of values can be modeled by an exponential function.
Finding the Equation
We see that exponential function of the form y=ab^x models the data. Notice that the constant ratio is 4, this is the value of b. Let's find the value of a by choosing one ordered pair from the given table and substituting the values of x, and y.
