Editing Exponential function (section)

==Compound interest==

The earliest occurrence of the exponential function was in [[Jacob Bernoulli]]'s study of [[compound interest]]s in 1683.<ref name="O'Connor_2001"/>
This is this study that led Bernoulli to consider the number
<math display="block">\lim_{n\to\infty}\left(1 + \frac{1}{n}\right)^{n}</math>
now known as [[Euler's number]] and denoted {{tmath|e}}.

The exponential function is involved as follows in the computation of [[compound interest#Continuous compounding|continuously compounded interests]].

If a principal amount of 1 earns interest at an annual rate of {{math|''x''}} compounded monthly, then the interest earned each month is {{math|{{sfrac|''x''|12}}}} times the current value, so each month the total value is multiplied by {{math|(1 + {{sfrac|''x''|12}})}}, and the value at the end of the year is {{math|(1 + {{sfrac|''x''|12}})<sup>12</sup>}}.  If instead interest is compounded daily, this becomes {{math|(1 + {{sfrac|''x''|365}})<sup>365</sup>}}.  Letting the number of time intervals per year grow without bound leads to the [[limit of a function|limit]] definition of the exponential function,
<math display="block">\exp x = \lim_{n\to\infty}\left(1 + \frac{x}{n}\right)^{n}</math>
first given by [[Leonhard Euler]].<ref name="Maor"/>