SOLUTION: Explain how you can use first and second differences to identify an exponential function.

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Question 1090767: Explain how you can use first and second differences to identify an exponential function.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Using Differences to Determine the Model
By finding the differences between dependent values, you can determine the degree of the model for data given as ordered pairs.
If the first difference is the same+value, the model will be linear.
If the second difference is the same value, the model will be quadratic.
If the number+of times the difference has been taken before finding repeated values+exceeds five(common multiplication pattern), the model may be exponential or some other special equation. y+changes more quickly than x, and you never see the same y value twice.
example:
x|y
0|4
1|12
2|36
3|108
4|324

4..............12.................36...............108................324
..........8.................24..............72................216-> The first differences are not all equal. So, the table of values does not represent a linear function
....................16.............56................160 -> The second differences are not all equal. So, the table of values does not represent a quadratic function. Find the ratios of the y-values and compare
ratio of y- values:
12%2F4=3
36%2F12=3
108%2F36=3
324%2F108=3

The equation to represent this data is y=4%2A3%5Ex
Note that the ratio of values is the same between each set of numbers. This is an exponential equation.