Real uses of the constant e?
Answer:
The beauty of e is that it pops up ALL the time.
In electrical engineering, we use it all the time because e^ (-t/[tau]) makes up part of the answer for the charging of a capacitor/ current across an inductor:
For a capacitor-resistor circuit: V= Voriginal(1-e^(-t/[tau]) where tau = RC (resistance times capacitance). This is the rate at which the voltage of a capacitor changes, since the voltage across a charging capacitor is time dependent.
For an inductor-resistor circuit (RL circuit): I= Ioriginal (1-e^-(t/[tau])) where tau= L/R (Inductance over resistance). This is the rate at which the current over an inductor changes, since the current across an inductor is time dependent.
There's no accident in the similarity of these equations, it's because they're the result of solving a first order linear differential equation which involves the natural logarithm (ln). As the previous answerers have indicated, there are many other uses for e. In the real world (ie if you're not a mathematician), many of the equations you use that involve e use it because e pops up in the solution to many differential equations.
As for why e is so prevalent in modeling physical situations? It's probably partially due to the fact that the integral of 1/x is ln(x).
e is a lovely thing, don't knock it. I hope my answers and those of the other answerers help you understand the beauty of it.
statisticians
exp shows up all over in the sciences. Arrhenius rate laws use e, many differential equations solve to include e, radioactive decay/bacterial growth, so there are mmany places in the sciences where exp is used.
The function e^x is on of the most imprtnat terms in math, and it's used widly in almsot all applied math fields. It's used to solve engineering problems (especially the ones that have differential equations). For example, a water tank with a whole in it, if we need to calculate the time needed to have the tank empty we have to use that function. If we need to know the tension on a hanged cable, we also have to use it.
It's used in biology to calculate the growth of bacteria. It's used to calculate the decay of atoms. It's used in statistics when we need to calculate the growth of population. And so on.
yes i do e is a vowel i before e as it comes after c like cone or come so alots of careers use the constant e the constant e?is used in many ways in many words
*The compound-interest problem:
More generally, an account that starts at $1, and yields (1+R) dollars at simple interest, will yield eR dollars with continuous compounding.
*Bernoulli trials
*Derangements
*E in calculus
*Other characterizations of e are also possible: one is as the limit of a sequence, another is as the sum of an infinite series, and still others rely on integral calculus.
*Number theory
The real number e is irrational (see proof that e is irrational), and furthermore is transcendental (Lindemann–Weierstrass theorem). It was the first number to be proved transcendental without having been specifically constructed for this purpose (compare with Liouville number). The proof was given by Charles Hermite in 1873. It is conjectured to be normal.
*complex number.
*Computer culture:
In contemporary internet culture, individuals and organizations frequently pay homage to the number e.
For example, in the IPO filing for Google, in 2004, rather than a typical round-number amount of money, the company announced its intention to raise $2,718,281,828, which is e billion dollars to the nearest dollar. Google was also responsible for a mysterious billboard that appeared in the heart of Silicon Valley, and later in Cambridge, Massachusetts; Seattle, Washington; and Austin, Texas. It read {first 10-digit prime found in consecutive digits of e}.com. Solving this problem and visiting the advertised web site led to an even more difficult problem to solve, which in turn leads to Google Labs where the visitor is invited to submit a resume. The first 10-digit prime in e is 7427466391, which starts at the 101st digit. (A random stream of digits has a 98.4% chance of starting a 10-digit prime sooner.)
In another instance, the eminent computer scientist Donald Knuth let the version numbers of his program METAFONT approach e. The versions are 2, 2.7, 2.71, 2.718, and so forth.
*The mathematical constant e is the base of the natural logarithm. It is occasionally called Euler's number after the Swiss mathematician Leonhard Euler, or Napier's constant in honor of the Scottish mathematician John Napier who introduced logarithms. (e is not to be confused with γ – the Euler–Mascheroni constant, sometimes called simply Euler's constant.) The number e is one of the most important numbers in mathematics,[1] alongside the additive and multiplicative identities 0 and 1, the imaginary unit i, and π, the circumference to diameter ratio for any circle in a plane. It has a number of equivalent definitions; some of them are given below.
Since e is transcendental, and therefore irrational, its value cannot be given exactly as a finite or eventually repeating decimal or continued fraction. The numerical value of e truncated to 20 decimal places is:
2.71828 18284 59045 23536...
*e is usually defined by the following equation:
e = lim (1 + 1/n)^n.
n->infinity
http://mathforum.org/dr.math/faq/faq.e.h...
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