- #1

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Thank you.

- Thread starter Master J
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- #1

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Thank you.

- #2

HallsofIvy

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If this particular layman has taken calculus, he/she should know that the derivative of any function of the form a

- #3

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yup e is just a plain old number.

i cant tell you where they got it but heres an idea.

if you deposit €1 in the bank at 100% interest for 1 yr you get €2

if they decide to compound the interest every 6 months you'll get:

€1.50 after 6 months, re invested at 50% interest to give you €2.25 at the end of the year

now the bank manager says, "how often would you like me to compound the interest?" and you think, this could be my shot to become seriously rich because obviousy the more often they compound it the more money you seem to get at the end of the year, so you say, "compound it infinatly often" and the nice bank manager says... "well...., for you,, ok"

after 1 year you look at you balance and you get

€2.71828.... in other words €e [ in other words ~$10 :D]

i cant tell you where they got it but heres an idea.

if you deposit €1 in the bank at 100% interest for 1 yr you get €2

if they decide to compound the interest every 6 months you'll get:

€1.50 after 6 months, re invested at 50% interest to give you €2.25 at the end of the year

now the bank manager says, "how often would you like me to compound the interest?" and you think, this could be my shot to become seriously rich because obviousy the more often they compound it the more money you seem to get at the end of the year, so you say, "compound it infinatly often" and the nice bank manager says... "well...., for you,, ok"

after 1 year you look at you balance and you get

€2.71828.... in other words €e [ in other words ~$10 :D]

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- #4

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2.7 € is not even $5 but never mind ...

- #5

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- #6

lurflurf

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Supose we have something (money, bugs, energy) accumulating exponentially

Thus rate of accumulation/amount=k a constant

in the amount of time it would take the stuff to double if growing at constant rate there is e if the growth is exponential.

suppose we can separate generations

1+1 +1/2+1/6+1/24+1/120+1/720+...

we se each generation is related by

a_n+1=a_n/n

and that the infinite sum converges to a transendential number approximately

2.718281828...

- #7

djeitnstine

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- #8

HallsofIvy

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And it is definitely not true that "the area under its graph is always the same". The area under the curve, from 0 to 1 is e, but the area under the curve from 1 to 2 is e