Question

What is `e` in Newton's Law of Cooling?

Answer 1

`e` is the base of the natural logarithm, that is, `lnx=log_ex`, where `e~~2.71828...` is a very special number that occurs a lot in nature.

In mathematics, there are also other special ways to represent `e` for example as the limit of a function

`e=lim_(x->0)(1+x)^(1/x)=lim_(x->oo)(1+1/x)^x`

or as the sum of an infinite power series

`e^x=sum_(n=0)^oox^n/(n!)` and so `e=sum_(n=0)^oo1/(n!)`.