E (Mathematical Constant 4)

Colorized Definition

\newcommand{\growth}{\color{c1}}
\newcommand{\naturallog}{\color{c2}}
\newcommand{\unitInterest}{\color{c3}}
\newcommand{\timetogrow}{\color{c4}}
\newcommand{\unitTime}{\color{c5}}

$$
\naturallog \ln(a)
\plain =
\timetogrow \int _{1}^{a}
\unitInterest {\frac {1}{x}} dx
$$
$$
\naturallog \ln(
\growth{e}
\naturallog )
\plain = 
\unitTime 1
$$

\naturallog The natural log 
\plain is 
\timetogrow the time to grow from 1 to a value
\\
\plain using 
\unitInterest 100\% continuous interest.
\\
\growth e is the number
\plain that takes
\naturallog the natural logarithm
\\
\unitTime 1 unit of time to reach.

Read More

• An Intuitive Guide To Exponential Functions & e (opens new window)
• Common Definitions of e (Colorized) (opens new window)
• Demystifying the Natural Logarithm (opens new window)