A little math problem

I have built a slider that for arguments sake is 100px long
and outputs a number from 0 to 100 depending on where you drag the
handle to. If you imagine a graph plotting the output against the
position of the slider handle it would be a straight line going
steadily upwards on a diagonal.
My question is this:
Can I set it up so that the graph would go up very slowly
until near the end and then suddenly rise sharply (I'm sure there
is a mathematical term for this type of curve)?
In other words if you dragged the handle from the 0 end over
the first 50px (50% of the total) the output would only go from say
0 to 10 then in the next 25px it would rise from 10 to 50 then in
the last 25px from 50 to 100.
I have played around with hard coding values and using
weighted arrays but this seems very untidy. I have also dabbled
with Math.log(), Math.exp() etc but my maths is pretty shoddy (as
you may have gathered from my rambling explanation of the issue :)
If anyone can shed any light on the issue it would be greatly
appreciated. I am fascinated by maths and its relation to patterns
and lines but it is all a bit above my head (at the moment)
Cheers all

y = (x^a)/(b^a)*b is the same as y = (x^a)/(b^[a-1]) , for
one thing. Not a biggie, but it might simplify things some
internally.
You might also try using what's called a piecewise function,
which is defined as different equations, depending on its input.
So, in your example, you'd want to define it as, say, x/10 for x
between 0 and 50; (x-10)/0.8 +10 for the second part, and
(x-50)*2+50 for the third part. It's not really elegant, but it's
pretty intuitive, which is important for learning new ideas.
If precise accuracy's not important and you just want to get
a curve going, an Excel spreadsheet is a quick and dirty way to get
an equation. Type in your known x coordinates in one column, and
the associated y coordinates in another column. Graph them, with
the XY (Scatter) type. Then, right-click on a data point, and click
Add Trendline. Play around with that, and be sure to select 'show
equation' and 'show R-squared value' under options. The closer
r-squared is to 1.0, the more perfect a match the displayed
equation will be.
Finally, I've found sosmath.com to be a good introductory
resource, and
http://mathforum.org/library/
looks fairly promising, as well.
Sorry if that's a bit of a brain dump, but I hope it helps
-Bob

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A little math problem

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