What are the applications of the number e?

Question

What are these applications in detail? How can the number be applied in math or science?

Answer 1

Hi,

e^x is a valuable function to understand because it (as well as it's counterpart ln(x)) can make many things easier to calculate. Here is a short list that is by no means complete:

Trigonometric functions (sine, cos, tan, ect...) can be converted to expressions involving e^x which makes them easier to manipulate.

The derivative of e^x is just e^x. Same for Integral, that doesn't come around very often, so we take advantage of it where we can.

Interest calculations usually involve exponential equations.
I(t)=Pe^(rt)

Where:
I(t) = Interest
P = Principal (what you borrowed or invested)
r = the interest rate.
t = the amount of time that you invested it.

Any time you have a set of data where successive points are further and further apart, the best way to model them is exponentially.

Hope that helps,
Matt

Answer 2

I should have a book to list all the uses of e

First in biology, when a population with unrestricted food develops, the development follows an exponential law where e is the base

N = No e^kt No population at time o , t time k constant

When a radioactive product decays the number of atoms remaining at time t

is n = n0 e^-lt where l is the radioactive constant (usually you use the Greek letter lambda, but i have it not)

Answer 3

e is a number which aproximatly equals 2.78. It is used primarily in equations such as those to calculate countinously compounding intrest (A=Pe^rt, where P is your principle, r is your rate, and t is time in years) This number is also used in many other equations that deal with popluation growth.

Answer 4

e does not really have "applications"; it just tends to turn up again and again throughout mathematics and related fields.

For instance, it is related to trigonometry, complex numbers, finance, geometry (spirals), electricity, calculus.

e is most interesting as the "base" of the natural logarithm.

Answer 5

http://mathworld.wolfram.com/e.html