I noticed this interesting fact during my secondary school education. Additionally you can use this to prove that e is the point where a change in the exponent

I noticed this interesting fact during my secondary school education. Additionally you can use this to prove that e is the point where a change in the exponent causes a larger result than a change in the base. E.g. (x+d)^y > x^(y+d) when y >= e for any real value d.