Function Growing Exponentially then Constant at X=0?

[germangb]

I have this function representation whch grows exponentially when it reaches X=0, but then it remains constant at some Y

does anybody know a function which looks like that?

 

[alberto7]

As an example of $\mathcal C^\infty$ but not analytic? As a way to glue $\mathcal C^\infty$-ly? Such a function is usually explained in Differential Geometry books in a section title Partitions of Unity.

 

[Mark44]

I have this function representation whch grows exponentially when it reaches X=0, but then it remains constant at some Y

does anybody know a function which looks like that?

Looks like a logistic function to me. See http://en.wikipedia.org/wiki/Logistic_function.

 

[zmp3]

Logistic Function.

 

[chiro]

Also:

http://en.wikipedia.org/wiki/Sigmoid_function

 

[Integral]

could also be the error function

 

[TGlad]

Unit step response of a damped harmonic oscillator? (It seems to oscillate a bit at its high point)

 

[germangb]

thank you all very much

 

[Peppino]

Sigmoid:

$y = \frac{1}{1+e^{-x}}$