Expression for Exponential Scale ?

If you want to work without keyframes, try this version of Mylenium's expression:

tStart=inPoint;
tEnd= inPoint + 2;// move time in seconds
tDiff=tEnd-tStart;
vStart=[10, 10];// starting Scale
vEnd=[70, 70];// ending Scale
vDiff=vEnd-vStart;
mStart=Math.exp(0);
mEnd=Math.exp(1);
mFac=linear(time,tStart,tEnd,0,1);
mMul=Math.exp(mFac);
vStart+linear(mMul,mStart,mEnd,0,1)*vDiff;

 The math does not match applying the Keyframe Assistants' Exponential Scale perfectly, but it looks pretty good.

Change line two to tEnd = outPoint, and the animation will last as long as the layer.

Something like this maybe:

t1 = inPoint;
t2 = outPoint - thisComp.frameDuration;
v1 = valueAtTime(t1);
v2 = valueAtTime(t2);
if (time < t1){
  v1;
}else if (time > t2){
  v2;
}else{
  d = t2 - t1;
  dv = v2 - v1;
  t = (time - t1)/d;
  v1 + dv*Math.exp(10*(t-1));
}

Something like this perhaps:

tStart=key(1).time;

tEnd=key(2).time;

tDiff=tEnd-tStart;

vStart=valueAtTime(tStart);

vEnd=valueAtTime(tEnd);

vDiff=vEnd-vStart;

vStart+Math.exp(tDiff)*vDiff;

Mylenium