I have the following data :
x=[1,2,3,4,5,6...,22]
y=[40, 50, 80, 100, 130, 170, 210, 250, 300, 360, 420, 490, 560, 630, 720, 810, 910, 1010, 1110, 1260, 1380, 1520, 1660]
I have observed the following:
y nearly doubles from 40 to 80 in 2 steps
y nearly doubles from 80 to 170 in 3 steps
y nearly doubles from 170 to 360 in 4 steps
y nearly doubles from 360 to 720 in 5 steps
y nearly doubles from 720 to 1380 in 6 steps
Hence I assumed that a good approximating function would satisfy
$f[0] = y[0] $
$f[i*(i+1)/2] = (2^{(i-1)})*f[0]$
What is $f$ then?
My guess is that $f$ looks like $exp(\sqrt x)$