A curve that starts with exponential growth and levels out

Question

I'm stuck on a mathematical problem in a small feature I'm building for a website. I need a function that starts out with exponential growth and than levels out as x grows. I've drawn this wonderful picture to communicate what I'm looking for since my math lingo isn't the best.

Any help appreciated.

curve

score 23 · Accepted Answer · answered Jun 15 '11 at 12:22

23

I think you want a sigmoid function.

answered Jun 15 '11 at 12:22

lhf

216,483

Thanks, solved my problem :) – Oscar Kilhed Jun 15 '11 at 12:44
Use these all the time for programming, easiest to use are logistic and atan – BlueRaja - Danny Pflughoeft Jun 15 '11 at 17:35
You say "starts out with exponential growth", so you want the logistic function. – starblue Jun 15 '11 at 20:13

Shai Covo · Answer 2 · 2011-06-15T13:28:00.390

3

Perhaps you are looking for something like ${\rm erf}(x-2)+1$, where erf is the error function, ${\rm erf}(x) = \frac{2}{{\sqrt \pi }}\int_0^x {e^{ - t^2 } dt} $. You can use WolframAlpha to watch the graph: plot $f(x)={\rm erf}(x-2)+1$, say from $0$ to $5$. Further see Wikipedia's plot of the error function, here, to understand the reason for choosing ${\rm erf}(x-2)+1$.

edited Jun 15 '11 at 13:28

answered Jun 15 '11 at 12:47

Shai Covo

24,077

A curve that starts with exponential growth and levels out

2 Answers2