What is e (2.718…) and why does it literally appear everywhere?
In: 756
well, strictly speaking, e is the number value where the slope of the graph of its exponential function (e^x) is the value of that function at any point on the curve. The slope at any point on the e^x curve will be the value of e^x. The slope and its value are the same everywhere. This is very useful and very convenient for a lot of purposes.
So, it is a special exponential function. Most functions are not like this (the slope of the function does not change at the same rate as the function itself), but math allows any exponential function to be expressed in terms of this special e^x function and some conversion factors, so any phenomenon that has exponential behavior will be able to be expressed by the special function. We like that special function because it is way easier to use when using higher-level mathematics to figure things out. This is why it appears everywhere, because exponential and logarithmic relationships exist everywhere, and the natural exponent and natural log behave mathematically in a simple-to-use way.
Do not need it, but it must exist (there must be some number that satisfies the requirement that the slope of the exponential function is the function itself), and once found, math became a lot easier in many ways, so it appears a lot in math. The value of e itself does not really much matter, the important thing is that there must be such a value. Once we know what that value is, lots of hard calculations become simple. Just plug it in.
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