What to do when "second differences" are different?

[MRF2]

Hey, I'm using data points:

X: -1; 0; 1; 2; 3
Y:-16; 4; 1; 1/4; 1/16

I solved for the first differences, and got:
-12; -3; -1/4; -3/16

I then solved for second differences, and got:
9; 11/4; 1/16

Is my math just wrong in a way I can't see, or...?
Thanks!

 

[Ackbach]

So, if the first-level differences are the same, you've got a linear model. If the second-level differences are the same, you've got a quadratic model. What do you have if the ratios are constant?

 

[MRF2]

So, if the first-level differences are the same, you've got a linear model. If the second-level differences are the same, you've got a quadratic model. What do you have if the ratios are constant?

Exponential model?

 

[MRF2]

Exponential model?

I didn't find the ratios to be the same.

 

[Ackbach]

Yes, it would be exponential if the ratios are the same. Is the first data point -16 or 16?

Hmm:
4/16 = 1/4
1/4 = 1/4
(1/4)/1 = 1/4
(1/16)/(1/4) = (1/16) * (4/1) = 1/4

So, if the first data point is +16 instead of -16, would the ratios be the same?