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
  1. 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(x-1) + 2(x-1)(x-2) + (11/6)(x-1)(x-2)(x-3) + (6625/3000)(x-1)(x-2)(x-3)(x-4) + (103/40)(x-1)(x-2)(x-3)(x-4)(x-5)
    = (1/120)(309x^5 - 4370x^4 + 23835x^3 - 61330x^2 + 73476x - 31680)

    posted by Steve

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