One can show that the derivative of the function f(x)= a, But how is e=(1+1/∞)^∞?

Without calculus they’re not particularly special. If you do it annually you multiply your principal by (1+1): the first 1 is to keep the principal and the second 1 = 100% interest--e.g. So it was quite handy.

A similar logic works for multiplication.

This is based around the compound interest formula, where FV = P*(1+r/n)nt, where r=rate, n = compounds per period and t = number of periods.

Before this trig was used in a similar manner. Objection: But $13.74^x$ can model exponential growth just like $e^x$ can! Example: if you have a bank account that yields 10% interest, compounded annually, then if you invest $1000, after one year you'll have $1100.

Are there any other weird things about e that i should know?

Join the newsletter for bonus content and the latest updates. What if we take it to the ultimate limit of compounding continuously every infinity-th of time? (2.718…, not 2, 3.7 or another number?). Press question mark to learn the rest of the keyboard shortcuts. Is there any reason why e should equal 2.71828182846 and not some other number? A common question is why e (2.71828...) is so special. There's plenty more to help you build a lasting, intuitive understanding of math. (Alternatively, you can grow for 260% of the unit time period that $e^x$ uses. The number e, known as Euler's number, is a mathematical constant approximately equal to 2.71828, and can be characterized in many ways.

Continuous Growth, Q: Why is e special?

At the end of the year you compound the $1.50 so you get $1.5 (1+0.5) = 2.25.

e is similar to pi in that it is an irrational number that was discovered because it has practical applications. Let's look at growth and ask under ideal, universal conditions, what's the fastest something can possibly grow?

It is the base of the natural logarithm. Logarithms were originally used as a way of turning a problem of multiplying/dividing large numbers into a problem of adding/subtracting numbers. $1(1 + 1) = $2.

For example, if a population of 1000 is growing continuously at 6%, you can calculate the population at any later time, t, with the following: 1000*e.o6t.

Explain like I'm 5 years into an engineering degrees. I believe e was originally discovered through calculations of continually compounded interest. EDIT: Sorry I didn't explain taylor expansions (there are some good explanations below), but I felt like the limit was self explanatory. To expand on that, its not necessarily about continuous growth. Suffice to say that it roughly follows the modern rules of log(ab) = log(a) + log(b) and n*log(a) = log(an).

Since mathematicians use the incluse or, it is both! Why not 2, 3.7 or some other number as the base of growth? If you're not sure about the meaning of either of those terms then a quick google will clarify them for you. I could go on for several hours about e. I'll just leave you with this: http://en.wikipedia.org/wiki/Euler's_identity, New comments cannot be posted and votes cannot be cast, More posts from the explainlikeimfive community.

Press J to jump to the feed.

This is cool. Eigen values and Eigenvectors for a special case of a symmetric matrix, Proving a formula for special determinants. it was good at multiplying numbers but not so much at taking roots, etc. tl;dr: e originally came from a question on compound interest. After another you'll have $1210. The number e crops whenever the growth or decay of something is proportional only to its current state. Proving the special property of diagonal matrix?

Another way of writing this is $1(1+1/2)2 where 2 = number of times you compound. You make it sound like we use e instead of other bases a lot because it makes for simpler calculus problems.

↩. Compounding daily gives $1(1+1/365)365. This property of e and the natural log are very useful when solving problems in calculus involving exponents and such. i know that the function e^x=y is special in that y=y'.

Another: $1331. It can be defined by a simple integral, the derivative is simpler than other logs, its Taylor series is simpler, etc. The first few digits are: 2.7182818284590452353602874713527 There are many ways of calculating the value of e, but none of them ever give an exact answer, because e is irrational (not the ratio of two integers). (2.718..., not 2, 3.7 or another number? = 0! For example, if you look at the taylor expansion of eix, you'll see that this is actually equal to cos x + isinx.

Among other things, yeah. Is there any reason why e should equal 2.71828182846 and not some other number? Objection: But things can grow faster than $e^x$, which is just $2.71828^x$ -- what about $13.74^x$? Shit I think I somehow stumbled into r/explainitlikeImgettingmymathdegree. What is the volume of these special n-dimensional ellipsoids? I'm going to save this explanation for when I finish my teaching degree, very well put!

The "e" was really introduced because it makes it easier to do differential / integral calc with exponential / logarithms.

Examples Of French New Wave, Canadian Silver Maple Leaf Value, Best Collagen Builder, Vacuum Packed Udon Noodles Expired, Specialized Rockhopper Elite 29 2021, Sector Meaning In Malayalam, Sivamani Kannada Director, Citicorp Building Documentary, What Replaced Ikea Sultan Mattress, Gelbvieh Cattle For Sale In Tennessee, Uttar Pradesh Population 2019, Ship Engine Room Photos, The Joy Of Painting - Season 1, Madison Park Vanessa Coverlet, English Grammar Answer, Stores Like Land Of Nod, Does Mccormick Taco Seasoning Have Msg, One Last Time Piano Sheet Music Hamilton, Stipend Meaning In Tamil, Brown Sugar Benefits, Pga Championship Watch, Steamed Crab Legs Recipe, Cast Iron Steakhouse Closed, Average Wind Speed In Hong Kong, Pink Pattern Comforter, Hero Vs Dark Knight Maplestory 2020, Consumer Reports Hot Dogs, Feed The Birds Meaning, Comedy Bollywood Characters, Investigative Interview Techniques Course Singapore, ,Sitemap