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I have 2 numbers 97 (F) and 415 (S) this is the key / legend.

Given any number (S), commonly between 200 - 900, I am looking for "F".

Where if (S) is above 415 "F" will be less than 97 and if (S) is below 415 "F" will be more than 97.

  • The higher "S" is the lower "F" is.
  • The lower "S" is the higher "F" is.

Here's some estimations:

  • 415 (S) gives 97 (F)
  • 612 (S) should give ~72 (F)
  • 514 (S) should give ~82 (F)

This is not a standard proportion as (F) of 612 (S) would be higher than 97.

What is this relationship called? How can I find the "F" of any number (S)?

ThomasReggi
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  • So, you are looking for a function $F = f(S)$, increasing on $S\in(200, 900)$, such that $f(415) = 97, f(514) = 82$, and $f(612) = 72$? Any number of functions have these properties. The "simplest" function I can think of at the moment is a quadratic. – Joshua Wang Nov 13 '20 at 02:43
  • If the relation is a polynomial, you can use the Lagrange Polynomial on a finite set of data values. If you have enough data, the interpolated polynomial will be the polynomial you are looking for. – RyanK Nov 13 '20 at 02:43

1 Answers1

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I believe I figured this out by doing this.

const getF = (S) => (1 / (S / 415)) * 97;
ThomasReggi
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