# Is there a name for this mathematical function? **URL:** \ **Category:** Factual Questions\ **Created:** [October 10, 2013, 5:07pm UTC](https://boards.straightdope.com/t/is-there-a-name-for-this-mathematical-function/670889 "2013-10-10T17:07:29Z")\ **Posts on this page:** 13\ **Page:** 1
**Author:** ![bibliophage](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bibliophage/32/7615_2.png) [@bibliophage](https://boards.straightdope.com/u/bibliophage)\ **Post date:** [October 10, 2013, 5:07pm UTC](https://boards.straightdope.com/t/is-there-a-name-for-this-mathematical-function/670889/1 "2013-10-10T17:07:29Z")
It’s a function of the form **x(t)=x[sub]0/sub**. It starts at x=0 at t=0 and approaches the horizontal asymptote x=x[sub]0[/sub] as t approaches infinity. It’s similar to the logistic function in that it approaches a horizontal asymptote, but I don’t think it’s the same. It shows up in physics in a few places, for example representing the increasing current in an RL circuit after a switch is closed or the increasing speed of a solid object falling through a viscous liquid under the influence of both gravity and drag. When I was in college, I learned about the logistic function, exponential decay, and exponential growth, but I don’t recall ever hearing a name put to this function. ---
**Author:** ![newme](https://avatars.discourse-cdn.com/v4/letter/n/e0b2c6/32.png) [@newme](https://boards.straightdope.com/u/newme)\ **Post date:** [October 10, 2013, 5:12pm UTC](https://boards.straightdope.com/t/is-there-a-name-for-this-mathematical-function/670889/2 "2013-10-10T17:12:31Z")
> [@bibliophage](#): > > It’s a function of the form **x(t)=x[sub]0/sub**. It starts at x=0 at t=0 and approaches the horizontal asymptote x=x[sub]0[/sub] as t approaches infinity. It’s similar to the logistic function in that it approaches a horizontal asymptote, but I don’t think it’s the same. It shows up in physics in a few places, for example representing the increasing current in an RL circuit after a switch is closed or the increasing speed of a solid object falling through a viscous liquid under the influence of both gravity and drag. When I was in college, I learned about the logistic function, exponential decay, and exponential growth, but I don’t recall ever hearing a name put to this function. Exponential decay. Looks like you left out the time component in your formula: **x(t)=x[sub]0/sub** ---
**Author:** ![bibliophage](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bibliophage/32/7615_2.png) [@bibliophage](https://boards.straightdope.com/u/bibliophage)\ **Post date:** [October 10, 2013, 5:18pm UTC](https://boards.straightdope.com/t/is-there-a-name-for-this-mathematical-function/670889/3 "2013-10-10T17:18:33Z")
Darn it. I meant **x(t)=x[sub]0/sub** When I think of exponential decay, I think of **x(t)=x[sub]0/sub** ---
**Author:** ![Sparky812](https://avatars.discourse-cdn.com/v4/letter/s/eb9ed0/32.png) [@Sparky812](https://boards.straightdope.com/u/Sparky812)\ **Post date:** [October 10, 2013, 5:25pm UTC](https://boards.straightdope.com/t/is-there-a-name-for-this-mathematical-function/670889/4 "2013-10-10T17:25:08Z")
Nerd Fight! 😃 ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [October 10, 2013, 5:45pm UTC](https://boards.straightdope.com/t/is-there-a-name-for-this-mathematical-function/670889/5 "2013-10-10T17:45:50Z")
I would just call it exponential decay as well, with the caveat that it’s decaying to a value other than zero. ---
**Author:** ![OldGuy](https://avatars.discourse-cdn.com/v4/letter/o/3bc359/32.png) [@OldGuy](https://boards.straightdope.com/u/OldGuy)\ **Post date:** [October 10, 2013, 5:50pm UTC](https://boards.straightdope.com/t/is-there-a-name-for-this-mathematical-function/670889/6 "2013-10-10T17:50:00Z")
Well it’s just a variation of exponential decay. Unfortunately it’s growing as it’s -x that’s decaying. If you think exponential decay would be misleading, the best name I can think of is bounded asymptotic growth, though there’d be ways to do that without the exponential function as well so that name might not be good if it’s the exponentiation you wish to emphasize. ---
**Author:** ![newme](https://avatars.discourse-cdn.com/v4/letter/n/e0b2c6/32.png) [@newme](https://boards.straightdope.com/u/newme)\ **Post date:** [October 10, 2013, 5:50pm UTC](https://boards.straightdope.com/t/is-there-a-name-for-this-mathematical-function/670889/7 "2013-10-10T17:50:03Z")
> [@bibliophage](#): > > Darn it. I meant **x(t)=x[sub]0/sub** > > When I think of exponential decay, I think of **x(t)=x[sub]0/sub** If you start with \*\*x[sub]0[/sub] \*\*atoms of Uranium, and want to know how many atoms of Uranium you have left at time **t** , the Exponential Decay formula is: \*\*x(t)=x[sub]0/sub \*\*If you want to know how many atoms have _decayed_ at time **t** , the formula is: **x(t)=x[sub]0/sub** I dunno that this second formula has a name. I would still call it exponential decay. ---
**Author:** ![Isilder](https://avatars.discourse-cdn.com/v4/letter/i/cc9497/32.png) [@Isilder](https://boards.straightdope.com/u/Isilder)\ **Post date:** [October 10, 2013, 5:55pm UTC](https://boards.straightdope.com/t/is-there-a-name-for-this-mathematical-function/670889/8 "2013-10-10T17:55:45Z")
> [@OldGuy](#): > > Well it’s just a variation of exponential decay… exponential to horizontal asymptote. ---
**Author:** ![Pasta](https://avatars.discourse-cdn.com/v4/letter/p/ecccb3/32.png) [@Pasta](https://boards.straightdope.com/u/Pasta)\ **Post date:** [October 10, 2013, 6:03pm UTC](https://boards.straightdope.com/t/is-there-a-name-for-this-mathematical-function/670889/9 "2013-10-10T18:03:28Z")
Not that you need another, but I concur. “Exponential decay”. It’s just slightly massaged to have the desired boundary conditions. This non-name would be akin to, say, f(x)=1+sin(x) not getting a name of its own but just being loosely called a sinusoidal function. ---
**Author:** ![bibliophage](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bibliophage/32/7615_2.png) [@bibliophage](https://boards.straightdope.com/u/bibliophage)\ **Post date:** [October 11, 2013, 7:47am UTC](https://boards.straightdope.com/t/is-there-a-name-for-this-mathematical-function/670889/10 "2013-10-11T07:47:34Z")
Thanks, folks. I bow to your collective wisdom. It still seems odd to call an increasing function a “decay,” but I guess I can reconcile myself to it. ---
**Author:** ![johnpost](https://avatars.discourse-cdn.com/v4/letter/j/f17d59/32.png) [@johnpost](https://boards.straightdope.com/u/johnpost)\ **Post date:** [October 11, 2013, 3:45pm UTC](https://boards.straightdope.com/t/is-there-a-name-for-this-mathematical-function/670889/11 "2013-10-11T15:45:33Z")
> [@Sparky812](#): > > Nerd Fight! 😃 slide sticks swinging, propeller beanies flying, pocket protectors ripped away. ---
**Author:** ![Pasta](https://avatars.discourse-cdn.com/v4/letter/p/ecccb3/32.png) [@Pasta](https://boards.straightdope.com/u/Pasta)\ **Post date:** [October 11, 2013, 7:47pm UTC](https://boards.straightdope.com/t/is-there-a-name-for-this-mathematical-function/670889/12 "2013-10-11T19:47:53Z")
> [@bibliophage](#): > > but I guess I can reconcile myself to it. If it helps reconciliation, no one in practice would actually refer to that function as “exponential decay” without lots of qualifying verbiage around it. The most precise answer to the original question is that there is no name for that function, but it’s in the class of “decaying exponentials” so in some categorical sense it is a decaying exponential. Contrast something like g(x)=1-sin(x). This also has no name, but one would be much more likely to call g(x) a sine function (with no weasel words) than one would be to call your function an exponential decay (with no weasel words). ---
**Author:** ![Napier](https://avatars.discourse-cdn.com/v4/letter/n/ce73a5/32.png) [@Napier](https://boards.straightdope.com/u/Napier)\ **Post date:** [October 11, 2013, 9:34pm UTC](https://boards.straightdope.com/t/is-there-a-name-for-this-mathematical-function/670889/13 "2013-10-11T21:34:53Z")
You could call it a relaxation function and say that it is relaxing toward some nonzero f(infinity) value.