what are some applications of e in mathematics?

Answer 1

EXAMPLE #1 CHEMISTRY & BIOLOGY;

Growth: N(t) = n0e^(kt) "n=number, k=rate, t=time"

Decay: M(t) = m0(1/2)^(t/h) "m=mass, t=time, h=half-life"

EXAMPLE #2 BUSINESS & ECONOMICS;

Compound interest
with e,"continuous": P(t) = p0e^(rt) "p=principle, r=rate, t=time"

EXAMPLE #3 SOCIAL SCIENCES;

Population Growth: P(t) = p0e^(kt) "p=populaton, k=rate, t=time"

These are a VERY few examples of the uses of e(exponential) in everyday life. As we go further in the mathematics/science field we'll encounter more highly sophisticated usefullness of e.

P.S. the letters used to symbolize subject may differ from individuals point of view but the function of growth & decay is mathematically the same.

Answer 2

The function f(x) = a*e^x (where a is an arbitrary value) is the only function that remains the same after you have taken the derivative of it.

If you power e by i*x, you will get a curve rotating counter clock wise around origo in the complex plane, at the radie 1, and with the absolute derivative 1.

Take -e, power it by an almost infinitely small number, subtract 1. The new number, e1 is a complex number. Calculate imag(e1)/real(e1).

If you are going to calculate the factorial (n!) of a number n, if n is a very large number, then n! / ((2*pi*n)^0.5 * (n/e)^(1/n)) = 1. So (2*pi*n)^0.5 * (n/e)^(1/n) is an approximate value to n!.

Answer 3

e is found practically everywhere in higher math. Not only is it the base of natural logarithms, it is also used to find values for the hyperbolic trig functions and pops up frequently in calculus & differential equations.

Answer 4

i've seen it in natural logarithms (the ln thing). it also calculates the value of accounts at a band that have interest compounded continuously.