Quanta Magazine: Why e, the Transcendental Math Constant, Is Just the Best

This says that the rate of change of ex is equal to its value at all points. When x represents time, it signifies a rate of growth (or decay, for negative x) that is equal to the size or quantity that has accumulated thus far. There are myriad phenomena in the real world that do exactly this for stretches of time, and we know them as examples of exponential growth or decay. …