I'd love to know how many people have swamped him with the correct answer so far. Any junior high physic student could answer this.
In fact, pick up a bouncy ball and drop it on a flat surface. You can observe the fact that bounces become smaller and more rapid, and then they stop bouncing entirely. There may be some residual vibration that is not apparent, but it sure seems to act like this toy model of the situation says it should.
Indeed, I've done that -- but my intuition told me that it was stopping due to friction, not due to the exponential decay of an infinite number of bounces. :-)
It's oddly disappointing to realize that the model actually acts more or less the same as the real world for once.
But your intuition was correct! Without friction the bounces would be perfectly elastic and wouldn't go into exponential decay! :-)