I cannot find the equation for this graph.

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doubled5
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I need it for a program I am writing. I found it all over the net but never with an equation. After two days I'm giving up and hoping someone recognizes it. It doesn't have to be exact I can fix it up but the profile needs to be the same.

Here it is:
 
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  • Line graph of a red curve plotted with horizontal axis from 3.0 to 8.0 and vertical axis from -100 to 100. The curve falls steeply from above 100 near x = 3.2, reaches a minimum of about -100 near x = 3.8, then rises gradually toward 0 and levels off near 0 by x = 8.0.
    equation.png
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That shape looks familiar, but not sure from what exactly. Physics or physical chemistry?

If you just want a function that fits the graph but you don't really know the mechanism making the shape, try polynomial function fit. Maybe third or fourth degree polynomial can give a good fit. Your graph shows fairly easily readable points. You'll only need the simplest of Linear Algebra skills to determine the function.