I'm having fun messing with (and breaking) some equations that relate to tweening and interpolation on linear input. What I would like is a simpler mathematical function to get a "tulip" shaped output. That is to say, given linear input, the output ramps logarithmically over the 1st quarter, then stabilises before ramping exponentially over the last quarter. This is vague, I know. I guess I'm looking for a reversed extreme cosine output; the following simple patch probably describes it better:
Forgive please, I am not math speaker good.