Something along these lines:
t1 = thisLayer.outPoint-framesToTime(20);
t2 = thisLayer.outPoint;
ease(time, t1,t2, value, value+[0,thisComp.height]);
Or maybe ease() could be easeIn() or easeOut(), depending on the timing you want.
If you need more control over the speed curve, then it can’t be done with a simple interpolation function.