Question

I have a value that i need to translate to a percentage given a certain set of rules.

VALUE=X

Where X can be anything starting from 0

If:

X > 200

the result of my function should be 100 (percent).

If:

X < 200 AND >= 100

the result should be between 100 and 50 (percent).
Example: X=150 would be 75%

If:

X < 100 AND >= 80

the result should be between 50 and 25 (percent).
Example: X=90 would be 37.5%

And if:

X < 80

the result should be between 25 and 0 (percent).

My approach in PHP would be something like

if($value > 200) return 100;
if($value > 100 && $value < 200) return ???;

… and so on.

Wherein ??? obviously stands for the formula i don’t know how to set up.

Is there a way to do this in one single formula?
And even if not – what is the mathematical approach to this problem?

I know it is very basic but it seems i skipped too many maths lessons in primary school.

Answer 1

The function can be defined piecewisely:

Graphically, this is represented with four straight lines of different gradients. While there isn’t a way to represent this function without separate pieces, implementing the above is quite easy.

In PHP, this function can be written as:

function f($x) {
    if ($x >= 200)
        return 100;
    if ($x >= 100 && $x < 200)
        return 50 + 50 * (($x - 100) / 100);
    if ($x >= 80 && $x < 100)
        return 25 + 25 * (($x - 80) / 20);
    if ($x < 80)
        return 25 * ($x / 80);
}