When teaching my students about the number "e", I would first start off with the history of "e" and Leonard Euler. Euler, a mathematician, gave "e" its name based on the following proof: 

For "m", which is arbitrary, we see the pattern shown in the picture for the expression (1+ 1/m)^m. 

As "m" reaches infinity, the expression (1+1/m)^m eventually equates approximately to 2.71 consistently, otherwise known as "e". Since (1+1/m)^m approaches "e", any positive base "b" can be written as a power of "e". For example, e^k=b. As a result of this, any exponential function f(t)=ab^t can be re-written in terms of "e" as f(t)=ab^t=a(e^k)^t=ae^kt. "k" can also be known as the continuous growth rate. 

When graphed as an exponential function, "e" would fall between Q= 2^t and Q=3^t. "e" is an important concept to know because it is necessary when calculating continuous interest rates in financial situations. It also helps in any equation that involves some sort of continuous rate.