How to mathematically introduce a function class of exponential decay?

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I am not a mathematician so I need help with a correct mathematic definition/description of a function /function class that I will be using for modeling through curve fitting. The function describes an exponentially decaying rate, something like:

$e^{-bx^p}+c$, $\ \ \ \ \ \ $ where a, c, b,p, x >0

Thank you in advance