Talk:Exponential decay

message: * OPPOSE the merge. Decay contributes to the half life. Not the same.
*I OPPOSE the merge to half-life.  They are not the same.  The half-life is a specific time that characterizes the decay curve.  It is used in physics and biology.  Engineers usually talk about the time constant.  Exponential decay is the process itself.  Also, one can have exponential decay to a non-zero value --dependent on the physical system modeled.  One doesn't usually talk about half-life in the context of exponential decay to a non-zero steady state value. Nephron 00:21, 19 March 2006 (UTC)
replies: text: It is possible to understand half-life without understanding the differential equation involved.  So, I think it is easier to keep 'em separate.  As for the duplication, it doesn't matter.  Wikipedia isn't a paper encyclopedia. Nephron 00:47, 22 March 2006 (UTC)
replies: text:  If you must know, not only have I read both pages, I've written and rewritten much of them.   The history of Half-life since last summer shows a repeating pattern of various people adding things and me removing them or trimming them down.  However, I've been a little more forgiving than I might have been. --Smack (talk) 06:44, 24 March 2006 (UTC)

text: It looks like we have a consensus.  I'll remove the merge tag. --Smack (talk) 19:27, 18 June 2006 (UTC)
thread_title:  Merge 

message: I was redirected here from Decay Constant, but this page doesn't seem to say all that much about the Decay Constant.  What is it?  Where does it come from?  What does it do?  (If anything)  How do you work it out?  I think this needs more explanation. --ayteebee (talk) 14:11, 22 April 2006 (BST)
:Can someone put up a definition for decay constant? -- mh 14:32, 4 August 2006 (UTC)
replies: text: See the very first line of the article. The decay constant is λ, the inverse of the time constant (which is the mean lifetime). The decay constant links the instantaneous absolute rate of decay to the amount of material, according to the differential equation which defines it, also seen at the beginning of the article. Perhaps if you could frame your question more specifically?  What is it you'd like to know?  The decay constant has units of 1/time. The time-constant and the half-life have units of time.SBHarris 18:40, 4 August 2006 (UTC)
replies: text: I was taught that the decay constant is the probability of radioactive particles that will decay in a second. Since the activity,  A = \frac {dN} {dt} = - \lambda N ,  \lambda = \frac {\frac{dN}{dt}}{-N} = \frac{-\frac{dN}{N}}{dt} , which is the probability of rate of decay of particles per unit time. This is what I was taught, but I'm not sure how accurate it is, since no site (that I have searched) seems to back this up.—Dudboi 10:17, 12 November 2006 (UTC)
replies: text: The equations you give are re-arrangements of those which appear in the article. And yes, the decay constant is the differential probability of decay with regard to time (in whatever units of time you're using). That is also the reciprocal of the particle mean lifetime (which is not the same as half-life). A particle which has a 0.01 chance of decay in any given time (say a second) will have a mean lifetime of 100 seconds (a collection will show this). SBHarris 22:20, 12 November 2006 (UTC)
replies: text: Indeed it is, so shouldn't we mention that it is the probability, rather than the inverse of the mean lifetime? After all, saying it is the inverse of the mean lifetime doesn't really explain what it's about.—Dudboi 01:24, 13 November 2006 (UTC)

text: Well, the equation is dN/dt = γN = [ln2/t(1/2)]N. If t(1/2) is 1.9e19 years = 6e26 sec and N is 2.9e27, then dN/dt is 3.35 disintigrations per sec. From here, you have to know that you need to calculate from the Poisson distribution the 0.05 probability time for 0 events, when gamma (expected event rate) is 3.35/sec, is exp-(γ*t), where the lamba here is the total expected event rate for our entire mass, not the one for each atom. So 0.05 = exp-(3.35*t). Solve for t and you get a time about 0.893 sec. You have to wait that long for a 95% chance to see a single disintigration with an expected rate of 3.35/sec. SBHarris 02:06, 28 July 2007 (UTC)

text: Okay, sorry about that, it's lambda isn't it. Forgot google could search symbols Phyte 22:53, 27 July 2007 (UTC)

text: Figured it.  Basically λ is a number such that the probability of decay in the next Δt seconds is Δλ.  When Δt is small compared to τ, it's fine to use it as "chance of decay per second", but when it isn't small, there can be a big difference.Andymc 18:27, 7 October 2007 (UTC)

text: "exponential decay if it decreases at a rate proportional to its value." The term rate is inexact here. The values at any time decrease at a constant "rate" (the decay constant), which means that the actual value of decay decreases also, the "rate", however, remains constant, or not, just whether you understand by "rate" the decay constant or the actual proportion. HJJHolm (talk) 10:40, 5 March 2012 (UTC)
thread_title:  Decay Constant?? 

message: Does anyone know if there's a variance or stdev associated with exponential decay?? y=Cexp(-x/λ)
for exponential prob. distribution y=λexp(-λx), the mean value is 1/λ and the variance is 1/λ² [ish!], but this distribution has only one parameter (λ), whilst exponential decay allows for 2 (C and λ).
insight greatly appreciated! Izzie— Preceding unsigned comment added by 131.111.85.79 (talk) 10:35, 1 June 2006 (UTC)
thread_title:  Errors/Standard Deviations 

message: These unsourced (subjective) statements have been deleted from the article, as per discusion of the terminology 
The concept of half-life is generally more traditional, particularly in the study of radioactive decay, where exponential decay first received the most study.  Although understanding the concept of half-life is generally easy, the additional logarithmic factor is now usually considered unattractive.  Most scientists and current textbooks are now opting for the mean lifetime over the half-life.  See the mean lifetime and half-life articles for more about their derivation and uses.
 
For the discussion of the terminology see 
Jclerman 19:16, 17 June 2006 (UTC)
thread_title:  Deleted statements 

message: I know that Request for Comment tends to be a place where people go when they are fighting, but I agree with Kjkolb's comment on Half-life that there should be a single place to discuss this, and I can't think of a better place to do it.  What do others think? Robert A.West (Talk) 11:55, 26 June 2006 (UTC)
thread_title:  Single place to discuss: RfC? 

message: I've had an editor revert the statement that time-constants, either the exponential time τ = 1/λ or the half-life t(1/2), function to keep the argument of an exponential unitless. People with a lot of physics training know this already (it's obvious), but is this article really written for THEM?  For the non-physicist and non-mathematician, it's helpful to point out that everything BUT the time in the argument needs to come out in units of 1/time, which is an easy way to see why λ must have units of 1/t.  The edit says, why not just SEE this?  My answer is, for that matter, why not just SEE that the solution of this extremely simple first order ordinary differential equation, is what it is? If you have much calculus, you don't NEED a derivation, so why not revert THAT? 
What's OBVIOUS and what's TRIVIAL depends on how much experience you have. But WHO is our audience?  It's only slightly more trivial mathematically that at any time t in a decay curve, τ = N(t)/[dN(t)/dt], so that you can quickly come up with τ, λ, t(1/2), etc. and thus you have these, any time you can evaluate your slope between two points, which is approximated by dN(t)/dt, the instantaneous decay rate evaluated at t.
In any case, please let us get a concensus on the question of who this article is written for (= target audience, both primary and secondary). I see it as a high school student or beginning pharmacy student who has had rudimentary calculus and maybe a little calculus based physics, or even none. But without deciding who our target audience is, we're destined to argue about this endlessly, because we're starting with different assumptions.SBHarris 18:06, 16 July 2006 (UTC)
thread_title: Explain unitless nature of exponential argument (WHO is our audience)??

message: i cant seem to see it mentioned anywhere here, so: 
Q(t)=a(1-r)^t
where                            
* the coefficient a is the initial value of Q (at t =0)                            
* the base b is the growth factor where + b = 1 – r is decay (0 < b < 1) where r is the rate (as a decimal)
* the exponent t is the independent variable
* the dependent variable is the quantity Q
Mokaiba (talk) 07:15, 26 September 2006 (UTC)
thread_title:  alternate general formula for decay 

message: QUOTING from the article: "In history of science, some believe that the body of knowledge of any particular science is gradually disproved according to an exponential decay pattern (see half-life of knowledge)."
This seems to me to suggest that (according to this belief) the sum of all scientific knowledge is decreasing over time.  Is this what is meant? It seems counterintuitive.
Wanderer57 (talk) 14:44, 7 August 2008 (UTC)
replies: text: I read it as that when a new field of science emerges, its beginning theories are quickly disproven, but over time, its theories remain stable. -- R'son-W (speak to me/breathe) 07:56, 8 November 2008 (UTC)
thread_title: Knowledge eroding?

message: The sentence on glottochronology was completely mistaken. 
The application of the exponential decay equation in glottochronology bears exclusively on the alleged steady decay of ONE language. To compute the time of split between TWO languages requires additional assumptions, which have nothing to do with exponential decay. HJJHolm (talk) 05:33, 18 May 2011 (UTC)
thread_title:  Social sciences - glottochronology 

message: Is it valid to say that the half-life is the median lifetime? Cesiumfrog (talk) 00:22, 6 February 2018 (UTC)
thread_title:  Median lifetime