McGraw Hill Glencoe Algebra 1, 2012
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McGraw Hill Glencoe Algebra 1, 2012 View details
6. Analyzing Functions with Successive Differences
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Exercise 9 Page 593

Calculate the differences and ratios between consecutive terms. Are either of these the same throughout the sequence?

Type of Function: Exponential
Function:

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.

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 values and compare them.
The ratios of successive 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.
We will use two ordered pairs given in the table to find the values of and For simplicity, let's use and We will start by substituting and for and respectively.
Solve for
We can write a partial equation of the function represented by the table.
To find the value of we will substitute for and for into our partial equation.
Solve for
Now we can write the equation of the function represented by the table.