1. Naming a function

Hello,

I have a quick question. What should I refer this type of function as when talking about it?:

$f(x)=\frac{c}{b-e^{k-x/a}}$

It is a sort of hyperbolic-exponential decay, but does someone know or have a better suggestion on how to define it?

Thanks

2. Re: Naming a function

Hey ImaginaryMe.

This kind of equations are known to have horizontal asymptotes (as x -> infinity)

Asymptote - Wikipedia, the free encyclopedia

In this situation, your function is going to approach c/b if a > 0.

There are classes of differential equations that satisfy these kind of things and some of them are relating to heating and cooling problems in Thermodynamics and have specific DE structures.

For this problem I suggest you find the DE that satisfies this equation and then see what kind of family this DE belongs to.

3. Re: Naming a function

I did in fact get this equation from a heating problem, which was originally a differential equation (the solution was a lot more complicated but this part was the most important - as it had the asymptote). The body is a solid though, not a gas, although I suppose it's a similar curve to adiabatic expansion, but that's too specific.

What I want is to describe (in words) this manner, represented by the function, in which the body loses it's heat and reaches the asymptote (equilibrium).

4. Re: Naming a function

I don't know any other generalization than horizontal asymptotic that would be too specific or too general.

You might want to look at fixed-point resources (i.e. fixed point mathematics books, papers, articles, etc) to get a description of something that has asymptotes in terms of the derivatives being equal to zero (and remaining zero) at a certain point which is something that is looked in non-linear analysis all the time (both in continuous and discrete time systems).

5. Re: Naming a function

Thanks for your help, but I think its not worth going to all the trouble for this. I was working on a physics project and I wanted to be able to name this type of decay I was seeing, but its not all that important.

6. Re: Naming a function

No worries, but one thing that is a real pain is doing what you are trying to do in the way of getting definitions.

It's really nuts how you get everyone "speaking their own language" and when you need to "translate" between the languages it becomes a nightmare and to me having to put too much effort into this exercise is just a waste of time for everyone involved, but unfortunately since everything is expanding so quickly it was bound to happen sooner or later.