"exponential something" : what is the name of that asymptotic exponential function?

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I'm wondering if there is an precise and clearly defined name for that kind of function :

$$ f(x) = A \cdot (1-e^{-\frac{x}{\tau}}) $$

It is an "exponential something", but definitely not an exponential decay, for sure, and not an exponential growth either, because it has an asymptotic behavior ... so what is his name ?

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