Trying to find a function to represent my data

Hello,

I'm trying to find the general form for a continuous function that will mimic the image I have attached. It is similar to a sigmoid function in the sense that it is flat initially and then has a very sharp transition, however it does not level out at the top, but rather increases continuously. Does anyone have any ideas as to what function may be appropriate?

Thank you for your help.

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Originally Posted by CLangford

I'm trying to find the general form for a continuous function that will mimic the image I have attached. It is similar to a sigmoid function in the sense that it is flat initially and then has a very sharp transition, however it does not level out at the top, but rather increases continuously. Does anyone have any ideas as to what function may be appropriate?
Attachment 24479

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Here is a possibility.

That certainly looks promising. What was the form of the equation?

Quote:

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Originally Posted by CLangford

That certainly looks promising. What was the form of the equation?

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$\displaystyle \[f(x) = \left\{ {\begin{array}{lr}{2\left( {\arctan (7) + 1} \right),}&{x < 4}\\{2\left( {\arctan (3x - 5) + 1} \right),}&{x \ge 4}\end{array}} \right.$
Now you can "play around" with those constants in the second condition.