The Snooze Button is Now a Math Problem

Yesterday I came across this problem while planning a lesson on ratio and proportion:

"When I woke up this morning, I hit the snooze button and got 10 extra minutes to sleep.  Every time I hit the button, I get 10 extra minutes.  At this rate, if my alarm first goes off at 5:30 and I hit the snooze button 4 times before I actually get up, what time do I get up?"

After careful thinking, it turns out that I wasn't actually interested in this problem at all.  I was actually interested in asking questions such as:

Does it make since to get 10 extra minutes every time you hit the button, or would it make more sense for the number of minutes to be related to the number of times that the button is hit?

Personally, I would love an alarm clock that gives me 10 minutes on the first hit, 8 minutes on the second hit, 6.4 minutes on the third hit, etc.  Then I could use this situation to talk about the limit of the time approaching zero.