Hi Kalid, thanks god, at last i can see a glimmer of light at the end of the long tunnel that is Acturaial CT1. I’ve been studying for the exam thinking that just my determination and drive would get me through it and this has been puzzling me since. Thanks so much for all you do for the wannabe maths wizzards that some of us are. Thanks. PS it would be great if you could put a word on the Force of Interest.
@Nelson: Great question, glad you enjoyed the article. Check out this article:
http://betterexplained.com/articles/how-to-develop-a-mindset-for-math/
The 2nd half covers different definitions of e, including “the derivative being the same as the origina function”. In a sentence, it’s another way to say “The rate of growth is exactly equal to your current amount: you are always growing at 100%”. e^x has several definitions depending on your point of view, just like a circle – hopefully the article above helps!
[…] students often find mathematics more accessible when coached in terms of money) can be viewed at: http://betterexplained.com/articles/an-intuitive-guide-to-exponential-functions-e/. Understanding exponential change has important social consequences (e.g, economic change, resource […]
thnks alot i hve been working on exponential growth and decay few days ago but not been able even to understand the concept bt this page really clears alot of my confusions
Explained very nicely.
Thanks a lot!!! your explanations are helping me to develop new mathematical models 
I call the dividends of excalibrator, compound disinterest, it is money paying a rent to humanity at large.
[…] my notes online and they envolved into this site: insights that actually worked for me. Articles on e, imaginary numbers, and calculus became popular, and made me realize how much we all craved deep […]
Kalid, I appreciate your help !! Thanks very much !!
[…] articles have awesome discussions, like understanding e. There’s gems, but unfortunately they’re buried inside hundreds of comments, which is […]
Thanks Jerry, glad it helped!
@ Jeremy Weiss
I think (in fact I’m nearly certain) you are mistaking a pre-calc supplement for a deep concept in a third year mathematics course in college. Unless you were lucky enough in high school you might have been given a fictional story about how a kid in your class uses pert shampoo to remember the formula A=Pe^rt. I wouldn’t take such rudimentary, although illusive, insights into e for granted.
@ Jeremy Weiss
I think (in fact I’m nearly certain) you are mistaking a pre-calc supplement for a deep concept in a third year mathematics course in college. Unless you were lucky enough in high school you might have been given a fictional story about how a kid in your class uses pert shampoo to remember the formula A=Pe^rt. I wouldn’t take such rudimentary, although illusive, insights into e for granted.
^^Clarification: it should be “an article for a deep concept…”. By no means do I think you mistook the two topics haha, just the audience this article was for.
Khalid, glad to see you still here. Below is my question/comment from 5 years ago. Your comments were lucid and spot on. I’m still on the transcendental number e, so here goes.
I actually think that I put too much prelude last time, and ended up being not clear, so here goes. Imagine a money in which every one is given and original allocation of 365 units of currency. On the the first day everyone is given one unit of currency. This represents 1/365 of the original allotment. The next day they receive a dividend that is 1/385 higher than the first day. This keeps its proportion to the total allotment constant at 1/365. If repeated over a year, the daily allotment will have grown to 2.74… (1 + 1/365)^365 a close approximation of e. The money supply will grow at the rate of the exponential function e^x. Money will have a half life(doubles) of about 8 months. In about 7 years it will have increased to 1,000 times in original amount. So the money is summed up into currency divisions that are 1,000 time the original. You cut three zeros off as Mexico did in 1993.
Another version is the 100% solution. Everyone is given an original allotment of 100 units. You may do with this as you please. Every account is taxed at the rate of 1% per day. This tax is distributed on a per capita basis.If you keep your account at 100 you receive exactly what you are taxed. If you have less you receive a net subsidy, if you have more you pay a net tax. This means that currency units deteriorate to the point of 1/e at the end.of 100 days. I call this the e period. I did not understand the math until I read you explanation of radioactive decay. The rate of decay is 100% in 100 days, but it is negatively compound as the elements are.
Your site is wonderful. I learned a lot here in a few minutes. I will be back.
My math site is mathfortheages.com and you mat find in interesting. My focus is on squares, square roots, the pythagorean theorem, the regular polygons and polyhedra.
My money is stuff is at different sites, mainly at usbig a group supporting a basic income or citizens dividend. excalibrator is designed to do that. google usbig and exclaibrator and that has the best article on that.
I will be looking over your whole website, and I think your explanation of e is the best I have seen. I have been negligent in not returning sooner.
stephen clark on October 17, 2007 at 4:14 pm said:
Kalid,
Thanks for the great explanation.
My comment is looking for a comment from you.
A new money system.
Every one gets 100 units a day for a year. At the end of the year there are 36,500 units of currency in circulation for each person. The 100 units have diminished as a proportion of the whole to the point of 1/365. On the first day of the second year the daily allotment is increased by 1/365. This keeps the proportion of the daily allotment constant at 1/365. Over year this approximates e, and if the growth is continuous, it is e. I call the type of money salmoney, and this particular version excalibrator.
I guess what I’m looking for is does this resonate with you as an apt or accurate use of e. Thanks for your time. My website is jaspersbox.com It is the attempt to create a new currency with a built in universal dividend.
Thanks for listening.
S. Clark
Kalid on October 17, 2007 at 11:26 pm said:
Hi Steven, thanks for writing, glad you liked the article. I’m not quite sure what you meant by “increasing by 1/365″ — do you want to keep the proportion of money handed out the same? (Even in the first case, giving out 100 per day, the percent changes day after day).
You can use e to convert between simple and compound interest — I’m planning on a follow-up article on this topic, which may do a better job of answering your question than I’m doing now
splendid!
you made so understandable
Bless you and thanks. I am not even a math student, only a curious reader. How many explanations have left me dizzy and frustrated!? I don’t understand it all, of course, but I did get enough through my head to congratulate you for your humane explanations. I’ll be studying and looking forward to more.
Hi Dewei, so glad it helped! The base “a” is how much you’ve grown at the end of each time period. So if you double at the end of a year, your base is 2. There’s more here:
http://betterexplained.com/articles/understanding-exponents-why-does-00-1/
Separately, it might seem natural to have 2 or 10 as a base (things double every year!). This is true, but only for human systems we can control, which only compound at the end of each interval.
Natural phenomena pay no attention to our calendars and are always growing at an instantaneous rate (such as 100% growth, compounded continuously). e^x is the best way to work with instantaneous rates.