SOLUTION: I have the following problem: Determine whether the function given by the table is linear, exponential, or neither. I understand how to determine if it's not linear

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Question 623564: I have the following problem: Determine whether the function given by the table is linear, exponential, or neither. I understand how to determine if it's not linear - take the ratio of the right column, look for a constant change. Now the solution given says to look at the values on the left of column and figure the ratio...here's lies the problem.
The table:
(x) f(x)
-1 1/9
0 1
1 9
2 81
3 729
They say (this is their example) : To begin, find the ratio of the first two consecutive outputs.
f(0)
_____ = 9
f(-1)
Then find the ratio of the next two consecutive outputs.
f(1)
______=9
f(0)

...and so on. What I don't understand is how they arrive at the ratio of 9 f(0) over f(-1) when the difference is only 1? Can anyone explain in laymans terms where the 9 comes from?
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

and

Where did you get the idea that the difference is 1?

Be that as it may: ; which is to say, the reciprocal of one-ninth is nine.

John

My calculator said it, I believe it, that settles it

SOLUTION: I have the following problem: Determine whether the function given by the table is linear, exponential, or neither. I understand how to determine if it's not linear - take the rat