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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!

  • 0
    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.2012-10-04

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What about $ x \mapsto \frac{100}{\pi/2}\arctan $?

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    I felt that the vertical tangent is not so important, and he was looking for these 6 characters: $\arctan$2012-10-05
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There are infinite solutions to your request, one can be

$ f(x)=100\frac{\sqrt x}{1+\sqrt x} $