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An example of a real life exponential function in electronics is the voltage across a capacitor or inductor when excited through a resistor. Another example is the amplitude aâ¦s a function of frequency of a signal passing through a filter, when past the -3db point.
Consequently, the exponential function with base e is particularly suited to doing calculus. Choosing e, as opposed to some other number, as the base of the exponential function makes calculations involving the derivative much simpler. Another motivation comes from considering the derivative of the base-a logarithm, i.e., of log a x for x > 0: