need help with exponential function

[lethal0r]

I am working with a set of numbers from 0 to 30.

I need to give each number an accuracy rating, 0 would be 0% accurate, 30 would be 100% accurate.

as a number gets closer to 30 the accuracy should increase exponentially, for example I would want the number 20 to be around 80% accurate.

I know I need some sort of curve to do this but am unsure how to create the function, can anyone help me out?

Tom

[ytswy]

I'm not claiming to be a maths guru, but it's a nice little problem so I'll have a go.

How about using a square root and converting it into a percentage?

sqrt(30) = 5.47722558, so if $x is the number you are trying to convert you could do.

sqrt($x) / 5.47722558 * 100

This would put 20 at 82%

Edit: this would put 1 at 18% and 4 at 32% and 10 at 58% - I'm not sure I've got what you are trying to achieve the right way around here..?

[phranque]

i just told myself i would stay out of these things!

you might consider using the natural laws of growth and decay which involve the natural logarithms and equations with "ln" and "e" in them...

i'll stop there

[ytswy]

hmm yeah, from what I remember you use log to make bendy lines straight. Presumably there is some kind of reverse log which can make straight lines bendy (I hope I'm not confusing anyone with my technical terminology here ;)).

[lethal0r]

thank you both. i will look into ln & e, no doubt this is going to hurt my head!