We are always oblivious of daily phenomena. For example, when we boil a cup of tea and then put it at normal room temperature, how fast is the water cooling down?
We don’t know. We intuitively think it should be proportionate to the temperature difference between the hot tea – close to 100 degrees versus the room – say about 25 degrees in Celsius. Experiments are conducted and verified our intuition is true, which is unusual in the scientific world.
So basically, this equation that the “Integral’s derivative equals itself” needs to be valid:
If f(x) is a value 2 powered by x, applying calculus formula as
h = 0.6931…
Now to mimic the situation of cooling down the hot water in a room environment, we want to force h = 1, and reversely compute the value c =
2.71828 … , it is thereafter named as e.
Certainly, if we try on equations other than the format of a value powered by a variable x, we can find other constant values. However, e is commonly and universally accepted now similar to the way we accept pie = 3.1415926…