Calculate an exponential function with 3 or more points

Question

Hello,

I have 3 points for example: (10/5) (40/3) (70/2)

And I want to write an algorithm to calculate the exponential function.

I found the "Gauß-Legendre-Integration" but I'm not that good in math to

understand that...

Have you any tipps on how to solve that?

The programming should not be the problem.

But I don't know how to start.