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 as a function of frequency of a signal passing through a filter, when past the -3db point.
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The current flowing through an electric circuit when you flick the switch on or off.
No, poop is a body function in which food is transformed. This is NOT a real life miracle.
Yes, Ultron is an example
yes, there are many, for example technology makes life easier and simple.
Value engineering refers to a system to improve the value of products by examining the function. Value is defined by a ratio of cost to function and value engineering is specifically defined in a public law.