Talk:Exponential growth

message: It looks like SARS didn't exactly grow exponentially as expected.  Maybe a different example would be better? ;) Revolver
How to invest?
 D'zeko (talk) 20:43, 15 September 2017 (UTC)
thread_title:  SARS 

message: The nuclear reactor example doesn't really work.  The damping of the control rods (hopefully!) prevents exponential growth in decay rate.  Needs work.--Rwinkel 15:56, 8 Aug 2004 (UTC)
thread_title:  Nuclear reactor example 

message: The opening paragraph still needs work. I seem to keep missing Michael Hardy's points, so maybe I'm not the best person to write it.  My understanding is that the usual case for an exponentially growing (as opposed to decaying) function is that it grows faster the larger it gets.  Of course, other functions can also do this, but exponentially growing ones always will.  Can someone supply a counterexample if that's not the case?  Lunkwill 22:17, 13 Apr 2005 (UTC)
replies: text: I'll return to this soon and do some work that's not as hasty as the terse edits I've done lately. Michael Hardy 02:22, 14 Apr 2005 (UTC)
thread_title:  increasing rate 

message: Week:     1   2
Option 1: 1c, 2c, 
We can describe these cases mathematically. In the first case, the allowance at week n is 2n cents; thus, at week 16 the payout is 216 = 32768c = $327.68. All formulas of the form kn, where k is an unchanging number (e.g., 2), and n is the amount of time elapsed, grow exponentially. In the second case, the payout at week n is simply n dollars. The payout grows at a constant rate of $1 per week.
<P> <P>
Please correct me if I'm wrong, but we need to correct for the ordinal numbering system here. Value at week n = 2^n-1.
<P>
p.
:Right you are. I fixed it, but you would have been most welcome to fix it, too. Incidentally, MediaWiki will almost always figure out what you mean without HTML tags, and you can sign your messages on talk pages if you want by putting 4 ~ characters in a row. Thanks for your contribution! Lunkwill 20:57, 4 August 2005 (UTC)
thread_title:  Correcting for the ordinal numbering system: 

message: Strictly speaking, if exponential growth requires a constant rate, then nothing grows exponentially. Why? Take the 3 logical cases:
1) positive growth rate. Nothing can grow indefinitely at a constant positive rate due to limits to growth. Any constant positive rate of exponential growth inevitably causes all available resources to be consumed, which then halts such growth!
2) negative growth rate. Anything which sustains a constant negative rate will cease to exist, which then halts all growth as whatever the "thing" was no longer exists!.
3) zero growth rate. It's not growing!
All quoted examples of exponential growth in this article are, in fact, temporary periods of constant rate exponential growth. Another way of saying that things grow via temporary periods of constant rate exponential growth is to say that they grow at variable rates of exponential growth. This is, of course, mathematical heresy because the definiton of exponential growth requires a constant rate!
But you can think of it this way:
*fixed rate compound interest = constant rate exponential growth
*variable rate compound interest = successive periods of constant rate exponential growth (at a potentially different rate per period) = variable rate exponential growth
Regards,
--Couttsie 01:17, 24 March 2006 (UTC)
thread_title: Nothing grows exponentially

message: Why the hell does geometric growth redirect here? Fresheneesz 05:57, 26 October 2006 (UTC)
replies: text: Because the two terms mean the same thing. -- Dominus 17:35, 26 October 2006 (UTC)
replies: text:  Well.. i'm not quite so sure about that, but since I have no other information to go on (couldn't find anything quickly), i'll put it up as a synonym, which should have been done if the term redirects here. Fresheneesz 22:52, 26 October 2006 (UTC)
replies: text: Are you sure they're always the same?  I have always thought so too, but lately I've run into a few (seemingly intelligent) articles that refer to them as different phenomena.  Always without explaining the difference, of course.  An unscientific Googling shows a bunch of articles saying things like "exponential (geometric) growth", and a bunch of others that include "the difference between geometric and exponential".  Anybody know math?  I don't.  JayLevitt 14:58, 15 November 2007 (UTC)

text: Dominus is right: geometric progression means a progression like 1, 2, 4, 8, 16 when a ratio between neighbours is the same in contrast with arithmetic progression: 2, 4, 6, 8, 10, 12, .. when difference between neighbours is the same. So geometric growth is y=2x - exponential function; and ariphmetic is y=2x - linear function. Guest 04:45, 18 January 2007 (UTC)

text: So is are discrete and continuous time different theories of time, or just different implementations of measurement?  In my world, I hear both terms applied to, say, the volume of growth a new server has seen. "Last month, we used to process one hundred messages a minute on that box; now it's two hundred a minute.  That's exponential growth!"  If [Randall Mundroe] swoops in with a cape and says "No, it's geometric, not exponential!" is he right or wrong, or just being unnecessarily deus-ex-machina?  —Preceding unsigned comment added by JayLevitt (talk • contribs) 08:09, 20 November 2007 (UTC)

text: No, I don't think I did -- but neither did I give a long enough example.  I was envisioning the server growing from 50 messages per minute to 100, to 200, to 400... JayLevitt (talk) 22:36, 26 August 2008 (UTC)

text: Here is an example that I have always seen to show that 'exponential' is a subset of 'geometric':  y=x^a is geometric but not exponential while y=a^x is both geometric and exponential.  I really think that Geometric should have its own page. Kmwalke (talk) 19:17, 10 March 2008 (UTC)
replies: text: I agree with Kmwalke, geometric growth is x^a not a^x JackAidley (talk) 16:55, 28 July 2009 (UTC)

text: So, Michael, do you have any example of geometric vs. exponential?  I don't understand the difference between discrete and continuous time, which may be the key here. JayLevitt (talk) 22:36, 26 August 2008 (UTC)
replies: text: See the article Geometric progression. The term 'geometric growth' is not used there, and I don't think it is widely used anywhere. The sequence is geometric, but the growth is exponential. Bo Jacoby (talk) 00:18, 29 July 2009 (UTC)
replies: text:  (In both of the above, the time variable is the exponent, not the base.)
* Polynomial growth, where the time variable is the base rather than the exponent.
Michael Hardy (talk) 00:46, 29 July 2009 (UTC)
thread_title:  geometric growth 

message: Given the previous posts...
----
=== What about a graph ===
I think we could use a graphic as an example for this article. There might be a good exponential one already on Wikipedia, so if anyone has the time to check out...  — Kieff | Talk 09:11, Oct 29, 2004 (UTC)
(wow, that's OLD!)
=== graph ===
apologies to the person who made it, but this graph is terrible. it looks like it was drawn with technology made obsolite 10years ago. the notiation is rather odd, and can you say pixilated? it could add clarity to the article, but instead left me temperarily dumbfounded. i drew better one, but alas i am too retarded to upload it. can so one better suited to the job fix this? mastodon 20:04, 1 December 2005 (UTC)
thread_title:  New graph 

message: apologies to the person who made it, but this graph is terrible. it looks like it was drawn with technology made obsolite 10years ago. the notiation is rather odd, and can you say pixilated? it could add clarity to the article, but instead left me temperarily dumbfounded. i drew better one, but alas i am too retarded to upload it. can so one better suited to the job fix this? mastodon 20:04, 1 December 2005 (UTC)
thread_title:  graph 

message: What do you call the growth rate that slows?
What if I had a million marbles, and a million plus the square root of a million marbles the next day, and that amount plus the square root of that amount the following day.  What's that?
Y'know, like rather than the graph curving up like one side of the Eiffel Tower, it would start steep and soon be only slowly increasing, like Uluru.  I'm talking about an ever increasing line where the rate of increase constantly slows rather than accelerating.  Any help?  Thanks. Gronky 18:47, 5 July 2007 (UTC)
replies: text: Exponential decay--Cronholm144 19:44, 5 July 2007 (UTC)
replies: text: Thanks for the response, but that doesn't seem to be what I'm looking for.  I'm looking for something that continually increases, just at an ever slowing rate.  Exponential decay seems to be in continual decrease. Gronky 19:47, 5 July 2007 (UTC)
replies: text:  You must have meant −e−x. Michael Hardy 15:12, 7 July 2007 (UTC)

text: Asking for a name for something that continues growing, but at a progressively slower rate, is not the same as asking for the "opposite" of exponential growth.  Nor is the latter question well-defined enough to admit any answer. Michael Hardy 15:11, 7 July 2007 (UTC)

text: The differential equation y'=\sqrt y has solutions y(x) = \left(\frac{x+C}{2}\right)^2. The difference relation y_{k+1} = y_k + \sqrt{y_k} has solutions of O(k^2), so the growth is called quadratic. --Petter 19:43, 30 October 2007 (UTC)
thread_title:  What's the opposite? 

message: Would Wikipedia be a valid example of Exponential growth, such as the number of wikipedia articles over time?--64.75.187.196 (talk) 09:50, 24 January 2008 (UTC)
thread_title:  Wikipedia? 

message: a number doesn't grow, according to the definition of number. Also other errors in same section:-
:: But "the number of people living is Slobovia" or the like does grow. Michael Hardy (talk) 15:30, 21 May 2008 (UTC)
replies: text: Correct. As drafted in the article it doesn't say number of (members of a set), so it can be easily confused with numeral. BTW number has some ten or more meanings... Quantity would perhaps  be more approapriate in the article. Jclerman (talk) 22:38, 21 May 2008 (UTC)
thread_title:  to be recast 

message: An odd example of exponential growth is your family tree, as you go backwards in time from yourself. It works like this. You have two parents, who each have two parents, who each have two parents....and so on. That's 2 ^ n for n generations. So, after "just" 64 generations, before you know it, the number of ancestors in just your family tree exceeds the number of humans estimated to have ever lived. 2^64 = 18,446,744,073,709,551,616 people in each living person's family tree 64 generations ago. That roughly 6.5 billion multiplied by 2 ^ 64. 
The example is odd because the number of ancestors being discussed are a) not necessarily unique individuals (some people occur in your family tree more than once - e.g. when second cousins marry second cousins) and b) this is not an example of a living population growing "forwards" in time, but a largely dead population (except many parents, some grand parents, and fewer great grand parents etc) increasing backwards in time. --Couttsie (talk) 09:47, 3 November 2008 (UTC)
thread_title: Generations in your family tree

message: Epidemics go under cubic relationships.  The poland v. france of russian capture-the-flag in greece.
- vampares  —Preceding unsigned comment added by Vampares (talk • contribs) 21:53, 31 January 2010 (UTC)
thread_title:  Re: SARS 

message: There used to be a quote of Albert Allen Bartlett in the opening paragraph of the entry: 
US scholar Albert Bartlett pointed out the difficulty to grasp ramifications of exponential growth, stating: "The greatest shortcoming of the human race is our inability to understand the exponential function." See also the author's video lecture: Arithmetic, Population and Energy.
Some IP address deleted it without explanation. I think it should be reinstated. I'll wait a couple of days for comments and then make the change if there are no objections.
MattKaymans  —Preceding undated comment added 16:22, 11 July 2013 (UTC)
replies: text: The quote should be in the article Albert Allen Bartlett, which is apparently already the case. I don't see why it would be relevant here. It might fit in an article such as sustainable development or sustainable living, though. Isheden (talk) 20:19, 11 July 2013 (UTC)
thread_title:  Quote in Opening Paragraph  

message: The first sentence currently reads:
:"Exponential growth occurs when the growth rate of the value of a mathematical function is proportional to the function's current value."
This means that, as the the functions value grows larger (eg. for larger x-values), the growth rate increases with this value.
However, also in the lead section, it is currently stated:
:The formula for exponential growth of a variable x at the (positive or negative) growth rate r, as time t goes on in discrete intervals (that is, at integer times 0, 1, 2, 3, ...), is
::x_t = x_0(1+r)^t
In this formula, r is a constant (ie. independent of the current value of the function x_t), and r is called the "growth rate" (ie. the same term as in the lead sentence).
Both statements together cannot be correct. I assume the problem lies within the usage of the term "growth rate". I believe that two different concepts were conceived in the two cases. In the first sentence, the author refers to the derivative of xt, which is clearly not the same as r.
Before making major changes to the lede, I wanted to hear at least one opinion (preferably of somebody who has helped developing this article). Tomeasy T C 20:20, 7 March 2015 (UTC)
replies: text: Yes, that was inconsistent. I changed it. - Patrick (talk) 22:18, 7 March 2015 (UTC)

text: Nigelj has put the inconsistent text back. - Patrick (talk) 22:36, 7 March 2015 (UTC)
replies: text: It's the second paragraph that is confusing you. The opening definition has remained largely unchanged since the first version of this article was created in 2003. It is consistent with the definition given in the first sentence of the Overview section of the more mathematical 'Exponential function' article. The part that's confusing you was added by  in 2011. Note that that formula comes from Compound interest#Simplified calculation. Its relevance to the lede section of this article is questionable in my opinion, and it is certainly true that the terminology used is not mathematically accurate. If you want to have a go at improving the second paragraph, or moving it down into the body of the article and into a better context, then I would support and assist where I can. --Nigelj (talk) 23:04, 7 March 2015 (UTC)
thread_title:  Growth rate constant or proportional? 

message: The "Examples" section has a line stating "Genetic complexity of life on Earth has doubled every 376 million years. Extrapolating this exponential growth backwards indicates life began 9.7 billion years ago, potentially predating the Earth by 5.2 billion years." The citation is .
The referenced page then says "The two researchers acknowledge their ideas are more of a "thought exercise" than a theory proposal. [...] Of course there are other possibilities to explain what happened [...] life could have evolved following Moore's Law during certain periods but not at others. [...]  There is also the possibility that the development of life had to reach a certain stage of development before it began to conform to Moore's Law. [...] There is the very real possibility that the beginnings and evolution of life don't conform to Moore's Law at all."
So basically, that paper says "we extrapolated small amounts of data to cover a much larger range, and in doing so made up a thing that's not true, but it might be."
No "thought exercise" should be cited as if it were fact, especially one that's on such obviously shaky ground.  This is a terrible example of "exponential growth".
(Unsigned)
:Agree.  I'll take it out if you haven't done so already. — Arthur Rubin  (talk) 20:17, 17 August 2015 (UTC)
thread_title:  Genetic complexity growth isn't exponential throughout history 

message: Says who that unbounded growth is not physically realistic? I think that needs references to back it up. I see no reason to think that exponential growth must stop at some point. The reasons cited in the article might not always happen. Yonathan Arief Kurniawan (talk) 06:26, 26 May 2017 (UTC)
thread_title:  Limitations of models 

message: So I've been using the hashtag #GeometricPopulationGrowth and noticed not many people use that hashtag -- at first I thought I misspelled it. Geometric growth redirects here but then isn't explained very well: In the case of a discrete domain of definition with equal intervals, it is also called geometric growth or geometric decay, the function values forming a geometric progression. Why doesn't "Geometric growth" redirect to "Geometric progression"? (Answer: Many people like myself mix up the two?) How about a paragraph in the article explaining the difference with simple examples? Google search has many links to "Geometric vs Exponential", here's a link for someone else who was confused about this article. Raquel Baranow (talk) 17:04, 11 October 2017 (UTC)
thread_title:  Geometric vs Exponential: how about a new subheading? 

message: The intro isn't clear at all to non-scientists. Can someone please rewrite it without using technical words like 'function' etc? :) Malick78 (talk) 23:54, 22 March 2020 (UTC)
thread_title:  Unclear intro 

message: What do you call it when a series increases at an exponential rate, but is not strictly exponential? For example, the currency series 1, 2, 5, 10, 20, 50, 100... obviously in the long run increases at the same rate as (10^1/3)^n, but the series is not exactly equal to any exponential formula. 2A00:23C7:548F:C01:89EF:1341:CEAC:CAFF (talk) 23:58, 30 January 2023 (UTC)
thread_title:  Is there a name for this?