what does exponentially mean

[madi]

if something is increasing exponentially

what does that mean?

i have an idea it is something about it increasing by increasing amounts over time
but i am not sure

ta

m
x

[Structural Integrity]

Exponentially means means that the growing speed is dependant on the time.
For example, think of bacteria multiplying... They double every minute.
In the beginning you have 1 bacteria.
After a minute you have 2
After two minutes you have four
etc etc...

However, this is not only for growth. Shrinking numbers can also happen exponentially. Think of the decay of radiation of a radiactive material. That is also an exponential function.

[queball]

Mathematically, that the rate of increase of a variable is proportional to the variable. Like money in a bank as you get interest, or number of people with AIDS as each infects a couple more.
http://en.wikipedia.org/wiki/Exponential_growth

More commonly anything that increases fast.

[Zar]

There are two people on the planet.

They have 3 children. (the adults die) - 3 people on the planet

These children have 3 children each (the adults die) - 9 people on planet

These children have 3 children each (adults die) - 27 people on planet

These children...... - 81 people on planet

These children..... 243 people on planet

These children..... 729 people on planet

This is an example of exponential growth. Where the next growth is faster than the previous growth which was faster than the growth before that.

Go to this site:

http://www.otherwise.com/population/exponent.html

Run the applet and view how when you keep the birthrate fixed at 1.5 (or whatever) the graph creates an upward, steepening curve. Watch how the fish multiply exponentially

[IncubusGod]

Dictionary.com usually helps too.

[meglamaniac]

In "proper" pure mathematics doesn't it mean something is increasing in the ratio of variable^e? You'll find the "e" button on your calculator if it's a scientific one.
I can't remember what e represents (because I hate maths and last did it at A level really) but it's something fundamental. If you hear scientists waffling on about exponential curves then that's what they mean.
The only thing I can remember is it's something repeated in the "real world" a lot (ie. the curve of wires between telegraph poles is based on e apparently).

But yeah it's more commonly used to mean something increasing at a power greater than 1 of itself.

[Jester]

Originally Posted by meglamaniac

In "proper" pure mathematics doesn't it mean something is increasing in the ratio of variable^e?

No. That would be polynomal growth. And a damn wierd case of it as well.

[wu_trax]

isnt e just a number, much like pi?

[meglamaniac]

Oops, didn't mean variable - meant the exact opposite in fact. Kindly substitute constant for variable. Doh.

Well yes of course e is a number, as are all other mathematical constants given algebraic representations. e was chosen because the value it represents is the so called natural exponent afaik.
e is just a number that happens to pop up in nature quite a bit, and so is considered "special" (see chaos theory and other things like that).
Basic info: http://www.ndt-ed.org/EducationResou...ath/Math-e.htm
Advanced stuff: http://numbers.computation.free.fr/Constants/E/e.html

[queball]

x = Ce^kt is the solution to dx/dt = kCe^kt = kx.
so if x = Ca^t = Ce^(t ln a) then k = ln a.

[madi]

Originally Posted by wu_trax

isnt e just a number, much like pi?

i think its about 2.72

[pablissimo]

Increasing by some constant factor raised to an exponent that's related to time, like when you're working out compound interest

[Ste]

e is the value that d/dx(e^x)=e^x

y=2^x is an exponential curve.

(editted so noone else points out my stupidity)

[Cyp]

Originally Posted by Ste

...

y=x^2 is an exponential curve.

If, and only if y=sin(x) is a straight line. Perhaps you meant y=cos(ix)-i sin(ix) is an exponential curve.

[Ste]

hmm, shows how much i know...
i'm gonna go hide.

[Dace]

a dictionary is your* friend

















*only true

[Androme]

Originally Posted by Ste

y=x^2 is an exponential curve.

Having just done logs and exponentials in further maths, that's one I've never heard of. The expoential curve is e^x therefore examples are 2^x not x^2 - these are all examples of the a^x group of curves.

[Ste]

yeh
read my next post

[BeeKiller]

Originally Posted by wu_trax

isnt e just a number, much like pi?

i believe, it's called the exponential number because it has a gradient of 1 at (1,1) or something like that, i know it has a gradient of 1 at an important coordinate but i'm not sure i've given the right coordinate there ^^
anyhows you can forgive me as i did my a level maths over a year ago

[Jennifer]

I'm almost crying here.

[meglamaniac]

Hear that?
That's the world's smallest violin, that is.