I need a bit of help with working out some maths.

I have a number somewhere between 0 and 200 that I want to map onto a
range between 500 and 250000.

This I can do with the calculation: mapped = (value * (249500 / 200))
+ 500

But now I want the mapped value to rise exponentially between 500 and
250000.  I.e. in a curved exponential rise.

I know PHP has the exp() function, could I somehow use this?
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