Make a formula based on a data table (Exponential function)

I always, since high school never found a good trick to do these kind of questions.

Lets say you've got a table (x and y)

X: 1 2 3 4 5 Y: 1 3 7 15 31

How can I make a function out of it? I know that it probably is a exponential function and that

y = 2(y-1) + 1

however I'm stuck there. I'm not sure how plug it all in. I really need help for those kind of question since I do those often. If there's any procedures to determine a function base on a data table please tell me. Thank you!

• Thanks alot. But ok, how exactly did you get there? Do you have any tips or procedures? – Delupara May 1 '16 at 20:01
• There can be infinitely many functions for a given table of course. One famous general method is known as Lagrange Interpolation Polynomials. You can type it directly into Wolfram (see example). – barak manos May 1 '16 at 20:02
• Also one unrelated question: How do I make a summation decrement instead of incrementing? Like this: $$\displaystyle\sum_{i=10}^{1} i$$ – Delupara May 1 '16 at 20:25
• How would that be any different then a "normal" summation????? Also, please publish whatever question you have in the proper manner (i.e., not in a comment to some other question of yours). – barak manos May 1 '16 at 20:33