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.

Nerd Fight!

I would just call it exponential decay as well, with the caveat that it’s decaying to a value other than zero.

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.

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.

exponential to horizontal asymptote.

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.

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.

slide sticks swinging, propeller beanies flying, pocket protectors ripped away.

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).

You could call it a relaxation function and say that it is relaxing toward some nonzero f(infinity) value.