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

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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!