"The" exponential function is ex. A more general exponential function is any function of the form AeBx, for any non-xero constants "A" and "B". Alternately, Any function of the form CDx (for constants "C" and "D") would also be considered an exponential function. You can change from one form to the other.
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Exponential relationship!
fundamental difference between a polynomial function and an exponential function?
The exponential function, in the case of the natural exponential is f(x) = ex, where e is approximately 2.71828. The logarithmic function is the inverse of the exponential function. If we're talking about the natural logarithm (LN), then y = LN(x), is the same as sayinig x = ey.
The number of atoms that decay in a certain time is proportional to the amount of substance left. This naturally leads to the exponential function. The mathematical explanation - one that requires some basic calculus - is that the only function that is its own derivative (or proportional to its derivative) is the exponential function (or a slight variation of the exponential function).