What is the constant e, the base for natural logarithms? Where do we initially come across with e?

Question

What is the usefulness of e? What the background that forced us to define the constant e?

Answer 1

e is roughly 2.718281828459045..the these first few decimal places tease some into thinking that ther eis a pattern, but there isn't: e is "transcendental" (like pi). We (mankind) initially come across with it from noting the limit of expenential fractions: consider a bank account where the interest rate is x% compounded annually. If you compound more often, the result is slightly more. It has long been established that the more often you compound, the higher the actual interest calculated. But there is a limit, and that limit (beyond which it cannot go) is e. The constant e crops up in calculus very often because of this relation to exponential expressions. Its use as the base of logarithms comes from this, and it is useful because it immediately links several exponential expressions to values that can be easily and directly calculated.

Answer 2

e arises in numerous mathematical and other applications. As said previously, it arises by integrating 1/x. In addition to the infinite series formula, it is also given by limit_{x to 0} (1+1/x)^x. Using Euler's formula, e^{i x}=cos x +i sin x, x=Pi, shows us that e^{i Pi}+1=0.

Euler was the first to prove that e is an irrational number--its decimal expansion goes on forever and ever and never repeats.

One of the most famous interesting applications is that the differential equation that describes exponential growth or decay, {dy/dt=k y,y(0)=y0} has solution y=y0 e^{kt}. In finance, you can use this formula to compute the value of an investment that compounds interest continuously. You can also use this formula to find the half life of a radioactive element or determine the age of an object being dated with Carbon-14 testing.

Answer 3

a twin of the apostle Paul traveled substantially to carry information of Christ to human beings in all aspects, committed ones in the present day are doing the same element. there have been tribes chanced on in the awesome one hundred fifty years that, contained in the awesome 2000 years, by no potential had any contact with Christians. Amazingly, although, they did have a legend of a depraved earth cleansed by employing technique of a global flood, with in ordinary words a handful of people surviving.

Answer 4

axproxiamately equal to 2.718. it first occur when someone try to integrate 1/x. this natural
number is very useful when calculating the half-life for radioactive disintergration.unfortunately bankers does not know how to make use of this natural number to determine how to calculate the number of years required to double your money, given a fixed interest rate.

Answer 5

e = 1 + 1/1! + 1/2! + 1/3! + ..... = 2.718.....

what is also interesting is that e to the power of (pi times i ) + 1 = 0