The number, e, is special. In the same way that pi is special for circles, e is special for many reasons. Its unique value is makes its exponential function give the value of its own slope and its own area under the curve. No other constant value, C , will do that. Try it ...
The demonstration only gives a rough approximation of the value of e. What is the value really? Why is this function, (e)^x , so useful?