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December 12th, 2016, 07:39 PM   #1
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Hello people,

I am writing a program (in java but not important), and I need to write a method (function) which is acting like math function f(x) which is described with following table:
X | f(x)
1 | 100
10 | 10
100 | 1
1000 | 1
10000 | 1
100000 | 1
.
.
. (F(X) ALWAYS 1 FOR NUMBERS GREATER THAN 100)

so, what I want to create is a math formula which has those results, so that I can implement it in my program.

Note: F(x) does not have to be exactly as stated in the table.
It can have +-20% deviation from the numbers stated in the table. For example: F(1) could be 120, f(10) could be 9.5, or anything like it, but in general it should be close to those numbers, and it should never go below 1.

I do not know how to create a math function which does that.

Plus, it would be great it the function does not include high level math in formula, because this formula should be implementable inside method in java programming language.

(additional information (not important for this question):
I am writing my own graphic user interface, and in that interface I am writing scroll bar class. Scroll bar class has size property. And I want the size of the scroll bar to be around 100 pixels in case I have 1 items in the list, around 10 pixels if I have 10 items, around 1 pixel if I have 100 items and more).


Anyway, does anyone know which math formula can give results similar to those in the table?

Thanxy.

Last edited by skipjack; December 13th, 2016 at 02:54 AM.
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December 12th, 2016, 08:22 PM   #2
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$1 + 129.225 e^{-0.266433 x}$

seems to do a pretty good job

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December 12th, 2016, 08:50 PM   #3
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HELLO ROMSEK,

YES IT DOES.
I DID NOT FIGURED IT OUT MYSELF.

YOUR FUNCTION f(x) = 1+129.225e−0.266433x IS WORKING GREAT. THANK YOU.

JUST, AS I SAID, IT CAN HAVE IN MY CASE UP TO +-20% DEVIATION FROM THOSE NUMBERS, SO ACTUAL FUNCTION I WILL IMPLEMENT IS:
1+129e−0.27x JUST FOR SIMPLICITY (BECAUSE IT TAKES LESS TIME TO EXECUTE IN COMPUTER).

THANK YOU.
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