Question is not clear. Are you asking for the functional form of the recovery gain that offsets a percentage loss? If so, you need to gain r/(1-r) following a loss to breakeven. I don’t know what you are talking about with the exponential thing.
What I mean is not the math behind the drawdown or the recovery but either the function of the the following chart that has in the x Axis the % of loss and in the y axis the % needed to recover from the loss.
As you can see the chart is a exponential function and I’d like to know what the function is. In other words i want to be able to subtitute de X value for 50% and the result of Y should be 100% meaning that if I loose 50% of equity I need a 100% increase from bottom to recover.