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29 Sep 2004, 09:33
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#1
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a little bit broken
Join Date: Jun 2003
Posts: 1,405
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what does exponentially mean
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
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i came, i saw, i made a bit of a mess
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29 Sep 2004, 09:40
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#2
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Rawr rawr
Join Date: Dec 2000
Location: Upside down
Posts: 5,300
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Re: what does exponentially mean
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.
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"Yay"
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29 Sep 2004, 09:42
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#3
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Ball
Join Date: Oct 2001
Posts: 4,410
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Re: what does exponentially mean
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.
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29 Sep 2004, 10:15
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#4
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Chief over all Monkeys
Join Date: Apr 2003
Posts: 1,771
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Re: what does exponentially mean
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
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29 Sep 2004, 10:18
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#5
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WANNASEEMYNEWCHAINSAW
Join Date: May 2000
Location: Éire
Posts: 2,738
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Re: what does exponentially mean
Dictionary.com usually helps too.
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I came, I saw, I shouldn't mix pleasure with carpentry.
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29 Sep 2004, 10:51
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#6
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Born Sinful
Join Date: Nov 2000
Location: Loughborough, UK
Posts: 4,059
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Re: what does exponentially mean
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.
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Worth dying for. Worth killing for. Worth going to hell for. Amen.
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29 Sep 2004, 11:14
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#7
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Pedantic hypocrite
Join Date: Jan 2001
Location: Back and to the left
Posts: 1,488
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Re: what does exponentially mean
Quote:
Originally Posted by meglamaniac
In "proper" pure mathematics doesn't it mean something is increasing in the ratio of variable^e?
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No. That would be polynomal growth. And a damn wierd case of it as well.
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I always wanted to be a dancer, but I could never get the shit off my shoes
.......
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29 Sep 2004, 11:17
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#8
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Registered User
Join Date: Jan 2003
Posts: 4,290
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Re: what does exponentially mean
isnt e just a number, much like pi?
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im not tolerant, i just dont care.
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29 Sep 2004, 11:35
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#9
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Born Sinful
Join Date: Nov 2000
Location: Loughborough, UK
Posts: 4,059
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Re: what does exponentially mean
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
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Worth dying for. Worth killing for. Worth going to hell for. Amen.
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29 Sep 2004, 11:53
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#10
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Ball
Join Date: Oct 2001
Posts: 4,410
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Re: what does exponentially mean
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.
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29 Sep 2004, 13:15
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#11
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a little bit broken
Join Date: Jun 2003
Posts: 1,405
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Re: what does exponentially mean
Quote:
Originally Posted by wu_trax
isnt e just a number, much like pi?
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i think its about 2.72
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i came, i saw, i made a bit of a mess
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29 Sep 2004, 13:18
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#12
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Henry Kelly
Join Date: Apr 2000
Posts: 7,374
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Re: what does exponentially mean
Increasing by some constant factor raised to an exponent that's related to time, like when you're working out compound interest
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You're now playing ketchup
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29 Sep 2004, 14:00
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#13
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Bored
Join Date: Apr 2001
Location: Nottm ->Shef ->Croydon ->Manc ->Durham ->Sheffield
Posts: 6,506
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Re: what does exponentially mean
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)
Last edited by Ste; 29 Sep 2004 at 18:35.
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29 Sep 2004, 14:22
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#14
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∞+♪²
Join Date: Nov 2000
Location: :uo!te]o¯|
Posts: 428
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Re: what does exponentially mean
Quote:
Originally Posted by Ste
...
y=x^2 is an exponential curve.
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If, and only if y=sin(x) is a straight line. Perhaps you meant y=cos(ix)-i sin(ix) is an exponential curve.
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29 Sep 2004, 15:11
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#15
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Bored
Join Date: Apr 2001
Location: Nottm ->Shef ->Croydon ->Manc ->Durham ->Sheffield
Posts: 6,506
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Re: what does exponentially mean
hmm, shows how much i know...
i'm gonna go hide.
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29 Sep 2004, 16:54
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#16
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so f*cking zen
Join Date: Jan 2003
Location: Hitting Bottom
Posts: 8,499
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Re: what does exponentially mean
a dictionary is your* friend
*only true
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On a long enough timeline, the survival rate for everyone drops to zero.
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29 Sep 2004, 18:22
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#17
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☆ ♥
Join Date: Jan 2003
Posts: 3,489
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Re: what does exponentially mean
Quote:
Originally Posted by Ste
y=x^2 is an exponential curve.
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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.
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29 Sep 2004, 18:34
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#18
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Bored
Join Date: Apr 2001
Location: Nottm ->Shef ->Croydon ->Manc ->Durham ->Sheffield
Posts: 6,506
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Re: what does exponentially mean
yeh
read my next post
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29 Sep 2004, 19:08
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#19
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Theh Muffin Man \o/
Join Date: Nov 2000
Location: On your left...., no, your other left stupid
Posts: 92
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Re: what does exponentially mean
Quote:
Originally Posted by wu_trax
isnt e just a number, much like pi?
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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
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29 Sep 2004, 20:55
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#20
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Destroyer of Worlds
Join Date: Feb 2002
Posts: 552
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Re: what does exponentially mean
I'm almost crying here.
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29 Sep 2004, 23:11
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#21
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Born Sinful
Join Date: Nov 2000
Location: Loughborough, UK
Posts: 4,059
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Re: what does exponentially mean
Hear that?
That's the world's smallest violin, that is.
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Worth dying for. Worth killing for. Worth going to hell for. Amen.
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