math
What is the rule for this function?
input 1 output 2
input 2 output 5
Input 3 output 12
Input 4 output 34
Input 5 output 135
Input 6 output 741
asked by
Rima

e^x:
2.718
7.389
20.08
54.598
148.413
403.428
so, it grows faster than e^x as x gets large
maybe e^(kx^2) can be adjusted some. Since it is not at all obvious (to me), and since there are only 6 data points, it will be e possible to fit any suitable polynomial or exponential.
For example, Newton's divided difference method fits
f(x) = 2 + 3(x1) + 2(x1)(x2) + (11/6)(x1)(x2)(x3) + (6625/3000)(x1)(x2)(x3)(x4) + (103/40)(x1)(x2)(x3)(x4)(x5)
= (1/120)(309x^5  4370x^4 + 23835x^3  61330x^2 + 73476x  31680)
posted by Steve
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