Eli5: Why are exponents so common in scientific formulas? Why is it so common that numbers in nature are multiplied by themselves?
In: Mathematics
Three general reasons:
1. Calculus. As you make derivatives and antiderivatives (say, distance, speed and acceleration), you often end up with exponents because that’s how calculus works. And the world seems to just work that way.
2. Because something behaves exponentially. One example is where the rate of change is proportional to the amount of the thing, for example population growth. The function that describes that mathematically is an exponential function. Another is diffusion (Arrhenius law), which increases exponentially with temperature.
3. Best fit methods. When you have a whole bunch of data you usually want to find a pattern it follows so that you can both describe it to others, and fill in the gaps where convenient. If you’re lucky, it’s linear. But more often than not you’re going to use an exponential 9r polynomial function to get the best fit. And those involve exponents. But it’s seriously just a choice in this case. You could do weird things with sines and cosines, or any other mathematical functions if you wanted. But exponental and polynomial functions are just easy to work with.
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