Motion editor and tweens are driving me crazy

It seems simple but i cant get it to work right.
I want to alpha tween (ease in from 0 to 1) an object on stage over 25 frames. And after the tween is over i want the object to persist on the stage and in the timeline. How can i do that?
afaik i have to extend the tween in the timeline beyond the keyframe with 1 alpha. But when i do that this also extends the time of the tween from 0 to 1 and it actually lowers the alpha 1 in the keyframe automatically to some figure that fits with the ease in which apparently spans the entire tween.

Help me achieve this simple thing. Pleaseā€¦