Thanks Ganesh!
Hi to everyone, this is my first post, because I REALLY need help.
Everywhere i see know this advertisements about Forex thing, got attracted, started to read about it, but still really confused about What is forex .
All the explanations i find on the internet are very complicated. Too many smart words.
Can someone explain what is forex by his own words ?
Tired of websites.
Thanks.
[…] read and then comment (here) on this blog post: http://betterexplained.com/articles/an-intuitive-guide-to-exponential-functions-e/ This entry was posted on Tuesday, February 21st, 2012 at 9:41 am and is filed under scribe […]
@Lin: Glad you liked it! Ack, that situation is all too common. Even if the teacher is excited and enthusiastic, they can still not explain it in a clear way. Unfortunately, we’re afraid to say the emperor has no clothes (“Nope, still not seeing it!”).
Please, tell me, As it applies to myself,
“Get you hungry for more: In the upcoming articles, I’ll dive into other properties of e.”
When will you “dive into”?
Thanks.
Javier.
Hi Cody, the key to split interest into “n” parts and multiply it out. For earning interest every 6 months (i.e., 2 times a year) you get:
(1 + .5)^2 = (1 + .5) * (1 + .5) = 1 (original amount) + [.5 + .5] (the interest the original earned) + [.5 * .5] (interest the interest earned) = 1 + 1 + .25
You can “expand out” the multiplication for any n; for n = 5 you have (1 + 1/5)^5. However, it becomes cumbersome to track it like that when you can just compute the exponent. If you want to draw it out, divide the growth into 5 steps, and each step add a new interest element (Start with blue. Step 1: Blue earns Green; Step 2: Blue earns Green, Green earns Red; Step 3: Blue earns Green, Green earns Red, Red earns Orange; Step 4: Blue earns Green, Green earns Red, Red earns Orange, Orange earns Pink; Step 5: Blue earns Green, Green earns Red, Red earns Orange, Orange earns Pink; Pink earns Black).
Hi! you probably already read my comment about my essay paper! i was wondering if you could help me organize all my ideas to make it a little more simplistic! Thanks so much your website is great!
I’ve been looking for such an explanation for a long time now, much appriciated
imma go check some more articles out
many thanks for putting up this website
[…] off, take a break and learn about e’s evil twin, the natural logarithm. Original Article : http://betterexplained.com/articles/an-intuitive-guide-to-exponential-functions-e/Pinaki Bhattacharyya Tags: exponential, logarithm, mathematics (function() { var po = […]
Amazing, thank you so much. I’ve been trying to get a better understanding of what it is that i’m learning rather than memorizing formulae, your detailed explanations are a real help. Kudos!
After reading your explanation, I understand (I hope!) that e is a constant, because all rates of growth are equal to the growth at 100%, but they have been squeezed or stretched, lengthened or shortened to accommodate the variations. (Is that right?) Your comparison to pi made it clear to me- all circles have the same curve, whether they are the edge of a dime or the edge of the sun. Thanks very much!
how would i find the approximate equation of a line that is similar to a decaying exponential function? i have a line that does decrease over time at a slowing rate, though instead of constant decay it sometimes repeats numbers as y approaches 0, and actually does reach 0 as there cant be half of the unit that im using.
hopefully im making some sense here… instead of constant decay, there is a chance of decay. so starting with one hundred, we lose alot, then some of those, some of the remaining until say, 2 are left. then those have a chance of going but dont for a few t units, then 1 left for a few times until it completely dissapears.
cheers!
Hi Moisés, great question. Your formulas have the rate as “-r” so we are shrinking. e^(-rt) is the formula for continuous, compound shrinking and (1-r)^t is the formula for compound but not continuous shrinking.
With continuous shrinking, we are shrinking at every possible instant. With non-continuous shrinking, the “shrinks” only happen at set intervals (every 3 months, for example). Check out this article for the difference:
http://betterexplained.com/articles/a-visual-guide-to-simple-compound-and-continuous-interest-rates/
Hi Coi, really glad it’s helping!
Thanks for the explanation!! I am a statistics major and I am embarrassed to report I do not know the explanation until today! Thanks!
@Martha: That’s pretty much it. e^x assumes 100% growth rate for time “x”. If you adjust the rate (50% growth, 200% growth) it’s like scalene e up and down (e^0.5x or e^2x), which is like changing the radius of a circle (to shrink it to a dime, or expand it to the sun). The core pattern is the same.
Hi Mikala, that’s awesome! I love it when people can share their knowledge with others :).
Khalid, Great article. But I am confusing myself. I thought i understood it but as I thought more and more about it I have confused myself.
Take following example -
If I have $1 that grows at a rate of 200% in 1 year with TWO time period (i.e. 100% per 1/2 year). by e ( rate * time) this will be e^2. But if I use your Mr Blue/Mr Green theory this gives me an answer of $4 ( if I have done it correct). I think I am missing something here. Please can you help?