The+number+e+-+Jun+Woo+H.

History:
The number “e” represents an irrational number in logarithms, and is commonly used to solve exponential equations. Now, you might wonder, why would mathematicians use an irrational number to solve mathematical problems? None of the mathematicians of the past have found a n y patterns to make this number “e" as a rational number. With this irrational number, we can solve m

[[image:euler.png width="181" height="224" align="right"]]
any mathematical problems, from Algebra to Calculus and even use it to calculate values of money in real life! Well, lets see!

“e” is also known as Euler’s number, as it was discovered by a man named Leonhard Euler. How he approached this number was through the equation (1 + 1/n)^n. Under the assumption that the variable n extends its value to infinity, it gives off the irration al number of e = 2.718281828459045235. To reach this number, Euler went through a process like this: e = 1 + 1/1! + 1/2! + 1/3! + until 1/infinity!.


 * In this case, the symbol ! is not used for an exclamation mark, but it is a symbol for what is known as a factorial. Factorial means to multiply the number with its descending numbers. For example: 3! would mean 3 x 2 x 1, and 10! would mean 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1.

Euler also attempted to find “e” through the method of expansion and approached in two ways: and



At the end, Euler found out that all of these end up in a pattern very close to the number 2.718281828459045235, which is an irrational number.

The number “e” can be used very effectively in real life!
The number “e” can be used to calculate the amount of interest income. A man named Jacob Bernoulli discovered that when interest is payed more often, the total income increases. For example, if someone invested $200 in a company and receives a 100% interest per year, then the person would receive a $200 income for his/her interest. (Since 100% of $200 is $200, the money is doubled.) However, if the payment is done quarterly, then it goes like $200×1.254 = $488.28125... the reason is because in the formula Total Cost = D(1+r/n)^nt, where D equals the amount of money invested, r as the interest rate per year, n represents the number of times the interest was given, and t represents the time, which in this case is 1 year. Because (1+r/n)^n = "e", the formula becomes: Total Cost = De^t. In this case, the formula goes like this:

Total Cost = 200(1+(0.1/4)^1x4 =Total Cost= 200(1+(0.25)^1x4 Simplified: Total Cost=200 x 1.25^4

Now, if we compare the total cost of annually given interest and quarterly given interest it goes like:

Annually: Total Cost = 200(1+(0.1/1)^1x1 = $400

Quarterly: Total Cost = 200 x 1.25^4 = $488.28125...

Now, this shows that if interest is given quarterly, then there is about $88 of benefit. So, if you are thinking about becoming a businessman, think about the number “e”!

If you really want to know the true shape of the number "e" check out:
http://antwrp.gsfc.nasa.gov/htmltest/gifcity/e.1mil

Learn How the number "e" is used in algebra!
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 * "The number e." //MacTutor History of Mathematics//. N.p., n.d. Web. 14 Jan. 2010. .
 * " YouTube - Algebra 2 8.3 Part 1 Examples The number e ." //YouTube - Broadcast Yourself.// . N.p., n.d. Web. 17 Jan. 2010. .
 * "e (mathematical constant) - Wikipedia, the free encyclopedia." //Wikipedia, the free encyclopedia//. N.p., n.d. Web. 14 Jan. 2010. .
 * "e - Euler's number." //Math is Fun - Maths Resources//. N.p., n.d. Web. 14 Jan. 2010. .
 * "e.gif." //Theanticmuse//. N.p., n.d. Web. 17 Jan. 2010. .