NOVEL THINKING

Is there any reason why e should equal 2.71828182846 and not some other number? However, when you start using derivatives and integrals (calculus) you find that e and the natural log are indispensable and surprisingly natural. I'm not entirely sure of the rationale behind the name. There's plenty more to help you build a lasting, intuitive understanding of math. Weekly, daily, hourly, minutely, secondly, etc. There are many ways of calculating the value of e, but none of them ever give a totally exact answer, because e is irrationaland its digits go on forever without repeating. But what assumptions did you make to get 13.74? e is similar to pi in that it is an irrational number that was discovered because it has practical applications. At the end of the year you compound the $1.50 so you get $1.5 (1+0.5) = 2.25. $1(1 + 1) = $2. It was discovered that as anything grows exponentially in a continuous manner, like a large population increasing, the rate it increases converges towards a specific number that will depend upon e. In other words, e is used to calculate continuous growth. Compounding daily gives $1(1+1/365)365. Now let's say it's compounded semi-annually (twice a year), We have after one year: $1102.5. = + + ⋅ + ⋅ ⋅ + ⋯ It is, but its more so about any time the rate of increase depends upon the number of items already there. But consider the benefits. With an arbitrary base b it turns out that the derivative of bx is bx * log*e(b), and the derivative of logb(x) is 1 / (x * loge*(b)) Because the logarithm of the base is always 1, e is the unique choice of base that simplifies these derivatives to ex and 1/x. So it was quite handy. So the slope at x=3 will be e 3. Here are 10 signs that will reveal you how special you are. You make it sound like we use e instead of other bases a lot because it makes for simpler calculus problems. (2.718..., not 2, 3.7 or another number? I believe e was originally discovered through calculations of continually compounded interest. In a real analysis class logarithms are defined simply as the inverse function of the exponential function. The way I heard it, this logarithm base is "natural" because it appears in the derivatives of every exponential or logarithmic function. Explain Like I'm Five is the best forum and archive on the internet for layperson-friendly explanations. The reason compounding it as 5% every 6 months earns more than 10% every 12 months is because the function an grows faster than the polynomial function na, for constant a and linearly increasing n. We make even more money if we compound every 3 months instead of every 6. Yes, you can beat $e^x$ in an exponential footrace, if you use a rate more than 100%. Press J to jump to the feed. Napier spent roughly 20 years creating tables of his "logarithms" so it could gain acceptance. A link is at the bottom. 1000 * e.06t @ t=1 gives you 1061.83. Without calculus they’re not particularly special. Why not 2, 3.7 or some other number as the base of growth? Why is 2.71828182846...etc special? Enjoy the article? The speed the function increases is the same as the function. Possibly it meant a way of doing division (ratio arithmetic?). Sure. level 2 For normal growth in a period t, with growth occurring only once in a period t, we get the growth formula, where P(t) = P(0)* (1+r)t, There might be something I'm missing here, but if I put $1000 in the bank and it grows at 6% per year - after 10 years the bank's going to have $1790.85 in my account every time and isn't going to cough up that extra $31.27. Before this trig was used in a similar manner. I read that e is "transcendental" (what the hell does that mean- some kind of hippie spiritualism thing?). Compounding monthly gives $1(1+1/12)12 = 2.61. Why not 2, 3.7 or some other number as the base of growth? What is it with you and 13.74? Jacob Bernoulli discovered it after asking, essentially, how much money you would get if you continuously compounded 100% interest on $1.00 of principal. i know that the function e^x=y is special in that y=y'. Why is 2.71828182846...etc special? But it isknown to over 1 trillion digits of accuracy! If you're not sure about the meaning of either of those terms then a quick google will clarify them for you. Continuous Growth, Q: Why is e special? I read that e is "transcendental" (what the hell does that mean- some kind of hippie spiritualism thing?). 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. To expand on that, its not necessarily about continuous growth. If you do it twice in a year then at 6 months it is $1(1+0.5)=$1.50. EDIT: Sorry I didn't explain taylor expansions (there are some good explanations below), but I felt like the limit was self explanatory. = 0! Another way of writing this is $1(1+1/2)2 where 2 = number of times you compound. Also, a kind of unrelated thing, why does 0!=1? Are there any other weird things about e that i should know? The idea was that 2 Cos(A)Cos(B)=Cos(A+B) + Cos(A-B). What is the volume of these special n-dimensional ellipsoids? It is the limit of (1 + 1/n) n as n approaches infinity, an expression that arises in the study of compound interest.It can also be calculated as the sum of the infinite series = ∑ = ∞! Being special could mean many things, like volunteering, helping your friends, listening to someone who feels alone, being a single mother or working all day long to pay the house mortgage. There must be some reason for why e=2.71828182846. The number e crops whenever the growth or decay of something is proportional only to its current state. Suppose you want to calculate the square root of a large number x. How do you take the derivative of a goddamn log? Instead of perfectly continuous, it's perfectly non-continuous (discrete), and we take growth step-by-step. First off, e was discovered, not chosen. Logarithms were originally used as a way of turning a problem of multiplying/dividing large numbers into a problem of adding/subtracting numbers. The number e is a famous irrational number, and is one of the most important numbers in mathematics.

Sodium Benzoate Formula, Rustic King Headboard Diy, Country Road Dresses, Micron Boise Salary, Childcare Leave Claim, Hot Cross Buns Origin Pagan, Mahesh Bhatt Children, Jazz Juniper Night At Masti, Best Blue Bell Flavors, Boisar Property Tax Online Payment, Soulmate List Of Qualities, Land For Sale In Coker, Al, Douglas Letter Wikipedia, Edward Jones Target Funds, Sugar Has The Same Effect On The Brain As, Cockle In Korean, Radio Frequency Radiation Symptoms, Pull Up Exercises, Filipino Chicken Recipe, Jools Oliver Net Worth, Mindfulness Coach Training, Pitch Angle Wind Turbine, Manhattan Comfort Liberty Entertainment Center, The Interesting Narrative Of Olaudah Equiano Answers, Ora Organic Net Worth 2019,