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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.
The derivative (rate of change) of the exponential function is the exponential function itself. More generally, a function with a rate of change proportional to the function itself (rather than equal to it) is expressible in terms of the exponential function.