LED DIMMING What is the approximate equation for this graph?

What is this line equation?

I am working on a led lighting project that will dim lights. linear dimming isn't working, because the middle values appear to be the same brightness...

The changes happen at the lower and upper values, so I'd like to use a relationship like is pictured in the upper graph of the picture, (not exactly exponential) but I can't remember what how to modify an exponential equation to get that result... I've had to guess, but it's a little off...

Any help would be appreciated?

Our eyes respond logarithmically to light level intensity, so a 10x increase in intensity looks about twice as bright. Look up logarithmic light intensity control.

..which means: instead of add/sub a number, use mul/div
change type to float.
To find factor, use n'th root steps you want for each decade (doubling)
eg. 1,21 will span 1..250 in 30 steps

Google "tweener", "easing", you may find what you want