Reply
Thread Tools Display Modes
#1
Old 06-21-2000, 05:50 PM
Guest
Join Date: Jun 1999
Posts: 15
I was a math major in college but it has been years since I have been deep into the subject matter. When using mathematical modeling in a simple Cartesian graph, what are the main differences between geometric and exponential growth? I knew this at one point long ago but I do not remember.
Advertisements
#2
Old 06-21-2000, 06:43 PM
Guest
Join Date: May 1999
Location: Columbus, OH
Posts: 1,223
In geometric growth, the change is discrete, while in exponential growth, it is continuous.

This site has a useful illustration and formulas:
http://fig.cox.miami.edu/~schultz/fall98/17res.html
#3
Old 06-22-2000, 08:05 AM
Guest
Join Date: Feb 2000
Posts: 265
I don't think so

Geometric growth has a constant rate of change - the increases per time period are constant.

Here's an example, with constant delta of 1
1, 2, 3, 4, 5, 6, ...

Exponential growth is where the rate of change is itself increasing.

In this example, each number is double the previous
1, 2, 4, 8, 16, ...

Russell
#4
Old 06-22-2000, 08:16 AM
Right Hand of the Master
Charter Member
Join Date: Feb 1999
Location: Chicago north suburb
Posts: 16,078
A better example, Russell, might be where the rate of change is 2.

The geometric growth is:
2, 4, 6, 8, 10,...

The exponential growth is
2, 4, 8, 16, 32,...
#5
Old 06-22-2000, 08:30 AM
AWB AWB is offline
Guest
Join Date: Jun 1999
Location: San Antonio, TX
Posts: 5,509
An Exponential function is a function of a constant number of exponential terms. It is a continuous curve; the exponents are from the set of real numbers

Exponential growth (one term):
Code:
f(x) = 2x
f(0) = 20 = 1
f(1) = 21 = 2
f(2) = 22 = 4
f(3) = 23 = 8
f(4) = 24 = 16
f(5) = 25 = 32
f(6) = 26 = 64
f(7) = 27 =128
f(8) = 28 =256
f(9) = 29 =512
Also
f(0.5) = 20.5 = 1.41...
f(-1) = 1/21 = 0.5
A Geometric function has variable number of terms, based on the argument. It also has a discrete graph. It may follow an exponential curve
Code:
 x
g(x) = sum 2x
 i=0
g(0) = 20 = 1
g(1) = 20 + 21 = 3
g(2) = 20 + 21 + 22 = 7
g(3) = 20 + ... + 23 = 15
g(4) = 20 + ... + 24 = 31
g(5) = 20 + ... + 25 = 63
g(6) = 20 + ... + 26 = 127
g(7) = 20 + ... + 27 = 255
g(8) = 20 + ... + 28 = 511
g(9) = 20 + ... + 29 = 1,023
But
g(0.5) is undefined
g(-1) is undefined
__________________
Merry Christmas from Courtney, the cutest child in the world!
#6
Old 06-22-2000, 01:19 PM
Charter Member
Moderator
Join Date: Jan 2000
Location: The Land of Cleves
Posts: 72,212
RusselM and CKDextHavn: What you describe as a geometric growth is actually what's referred to as an arithmatic growth. Gilligan got it right: The only difference between geometric and exponential is that the former is discreet, while the latter is continuous: For any geometric progression, you can find an exponential progression that matches it at all points where it is defined.
#7
Old 06-18-2013, 07:12 PM
Guest
Join Date: Jun 2013
Posts: 1
(sic)

Chronos....do you not mean discrete?
#8
Old 06-18-2013, 07:31 PM
D18 D18 is offline
Guest
Join Date: Jan 2001
Posts: 1,707
Wow! A zombie nitpick!
#9
Old 06-18-2013, 08:55 PM
Guest
Join Date: May 2000
Location: Brooklyn
Posts: 23,342
Quote:
Originally Posted by headbanger View Post
Chronos....do you not mean discrete?
I'm sure that 13 years ago, he did indeed mean discrete. But we can forgive Chronos this one trespass; he's more than made up for it over the past decade.
#10
Old 08-17-2015, 04:07 AM
Guest
Join Date: Aug 2015
Posts: 1
As a retired professional mathematician with a PhD in mathematics, I'm probably a reputable source.

A geometric progression (or sequence) is almost the same as exponential growth which is more properly called an exponential progression (or sequence).

A geometric progression starts with a number which I will call a and then is followed by numbers based on a number that I will call b as follows:

a, a*b, a*b^2,a*b^3,a*b^4 and so on. If it is a finite geometric progression it stops at some number a*b^k where k is a positive integer. If it is an infinite geometric progression it continues forever - meaning that there is no last integer k as there is in the finite example. For those who are interested this is a countably infinite sequence - the first infinity is countable infinity and it is the number of integers. This may seem strange, but the number of rational numbers, numbers which are the ratio of two integers m and n such that (m/n) is an irreducible fraction, although being irreducible is not necessary to what follows, is also countably infinite. In other words, the number of integers is the same as the number of rational numbers.

An exponential sequence starts out with a number and continues as follows: a, a^2, a^3, a^4... which again may be a finite sequence ending in some number a^k where k is a positive integer or it may be (countably) infinite, that is it keeps on going forever (see above).

Thus a geometric sequence starts with a number a and then is followed by multiplication of a number b as stated above. Since b can be the same as a, all exponential sequences are geometric sequences, but when a and b are different we have a geometric sequence which is not an exponential sequence. Hence the set of all exponential sequences is a proper subset of the set of all geometric sequences.

Addendum: The proof that the number of integers is the same as the number of rational numbers is fairly simple to comprehend, but it's too lengthy for this forum. If you google "prove that the number of integers is the same as the number of rational numbers" (no quotation marks), I'm sure that you will find a plethora of proofs.
#11
Old 08-17-2015, 08:09 AM
Charter Member
Moderator
Join Date: Jan 2000
Location: The Land of Cleves
Posts: 72,212
It's not that hard. The count of rational numbers is no greater than the count of ordered pairs of integers, since every rational number can be expressed as a distinct ordered pair of integers. And the set of ordered pairs of integers is equal to the set of ordered pairs of integers whose sum is 0, union the set of ordered pairs of integers whose sum is 1, union the set of ordered pairs of integers whose sum is 2, etc. So enumerate all of the ordered pairs of sum 0, all of the ordered pairs of sum 1, all of the ordered pairs of sum 2, and so on in that order.
#12
Old 08-17-2015, 03:47 PM
Guest
Join Date: Sep 2011
Location: Sunny California
Posts: 14,238
Quote:
Originally Posted by headbanger View Post
Chronos....do you not mean discrete?
No, he wrote discreet and he meant it. Such subjects are not to be spoken of in polite society, and for thirteen years, it wasn't.
#13
Old 08-17-2015, 04:31 PM
Charter Member
Join Date: Mar 2000
Location: Between pole and tropic
Posts: 7,544
Quote:
Originally Posted by Senegoid View Post
No, he wrote discreet and he meant it. Such subjects are not to be spoken of in polite society, and for thirteen years, it wasn't.
On the other hand, headbanger's nitpick while hardly discreet, was the essence of discrete - his one and only post on these Boards.
#14
Old 08-17-2015, 04:33 PM
Member
Join Date: Mar 2002
Location: KCMO
Posts: 11,103
I'm having a little trouble grasping this. The definition of discrete linked to in post #9, and the difference between discrete and continuous as used here, are not really making sense to me. Is it right that a discrete function can be likened to a series of dots that have spaces in between while a continuous one can be likened to a line?

Best I can figure, an exponential progression is a subset of the set of geometric progressions, and is for lack of a better word "pure." Is it right that x^2, x^3, x^4 etc. is geometric and exponential while 2x^2, 2x^3, 2x^4 etc. is geometric but not exponential?

I'm trying to keep it very basic, as I've found the explanations already offered to be confusing. I'm just trying to picture examples that convey the gist of it, so simple layman-oriented replies will probably be most helpful. Thanks.
#15
Old 09-28-2015, 04:35 PM
Guest
Join Date: Sep 2015
Posts: 1
Quote:
Originally Posted by friedo View Post
I'm sure that 13 years ago, he did indeed mean discrete. But we can forgive Chronos this one trespass; he's more than made up for it over the past decade.
friedo.....do you not mean this one indiscretion?
#16
Old 09-28-2015, 06:20 PM
Charter Member
Moderator
Join Date: Jan 2000
Location: The Land of Cleves
Posts: 72,212
Quote:
Quoth Gary T:

Best I can figure, an exponential progression is a subset of the set of geometric progressions, and is for lack of a better word "pure." Is it right that x^2, x^3, x^4 etc. is geometric and exponential while 2x^2, 2x^3, 2x^4 etc. is geometric but not exponential?
Both of those are geometric. In either case, you can ask questions like "What's the second term in the sequence?": As written, that would be x^3 or 2x^3. But you can't ask questions like "What's the 2.5th term of the sequence?", because they're not defined there. With an exponential, you can ask that question.
Reply

Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is Off
HTML code is Off

Forum Jump


All times are GMT -5. The time now is 11:41 AM.

Copyright © 2017
Best Topics: playgirl erections shooting two guns plastic bag suicide record speeds microdium crystals good luck hunting monky fuck 2000 quid 45 weeks pregnant directional emp biggest human poop 190 cc hp asswipe johnson tryhard meaning possum lodge motto sp mean what kills pigeons z zzz az personal bowling lanes wayne newton voice super tendon leg dent immune to poison jesus h laundry mark necromancy bible refrigerator vents cortana virus principle photography does zicam work how do you get a fever on purpose base metal bezel 1501 how to keep face warm in winter life expectancy of a heroin addict how do i know if i'm restricted on facebook lime in the coconut meaning i've never smoked but i crave cigarettes how high can you safely jump into water how long should plumbers putty dry usps parcel select ground vs priority mail super thick beard hairs champagne in the freezer what size uhaul do i need how to get the red cross to stop calling toothbrush holder for drawer standard roof truss spacing how much does a zeppelin cost bands with no original members how to open a window screen from the outside how do tracer rounds work which engineering major is the hardest is duct tape safe for dryer vents rid x for septic tanks pepperoni and cheese oregon trail how many songs does an ipod nano hold sexual side effects of cocaine two colors that make pink what is an iron chef by definition how do ship anchors work who owns kingsford charcoal turbotax federal free vs freedom how to shine corian countertop third day after surgery