How do the consecutive terms relate to each other?
Type of Function: Exponential Function: y=0.2(5)^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
-2
-1
0
1
2
y
0.008
0.04
0.2
1
5
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
Let's recall the general form of this type of function.
y=ab^x
We will use two ordered pairs given in the table to find the values of a and b. For simplicity, let's use (0,0.2) and (1,1). We will start by substituting 0 and 0.2 for x and y, respectively.
We can write a partial equation of the function represented by the table.
y=0.2b^x
To find the value of b we will substitute 1 for x and 1 for y into our partial equation.
