# Looking for simple function: Passes through 0, sqrt like but never reaches 100

It's in the title. I am looking for simple function that passes through 0, square root like, never reaches 100, but comes closer and closer to it.

I'm sure this is very basic, nothing fancy. But I don't know it now.

Thanks a lot!

-
What do you mean when you say "square root-like"? Do you mean that you need it to have infinite slope at $x=0$? Do you want $f(x)\approx \sqrt{x}$ when $x$ is small? Or do you just want a function whose slope decreases and which tends to 100 as $x$ tends to infinity? –  Chris Taylor Oct 4 '12 at 17:07
My question aims at: "whose slope decreases and which tends to 100 as x tends to infinity." I am basically trying to give a mathematical impression of a organism that recovers after a shock (0): First very fast, then slower and slower. –  Frank Oct 4 '12 at 17:14

What about $x \mapsto \frac{100}{\pi/2}\arctan$?
This function do not expose the vertical tangent at $x=0$ feature of $\sqrt x$. –  enzotib Oct 4 '12 at 17:01
I felt that the vertical tangent is not so important, and he was looking for these 6 characters: $\arctan$ –  Berci Oct 5 '12 at 10:39
$$f(x)=100\frac{\sqrt x}{1+\sqrt x}$$