[Frank Cox]

Based on my (brief) attempt at Android programming a few years ago, I was under the impression that modern Android apps aren't supposed to have a close or quit button.

Google just found me this:

Question: Does the user have a choice to kill the application unless we put a menu option in to kill it? If no such option exists, how does the user terminate the application?
Answer: The user doesn't, the system handles this automatically. That's what the activity lifecycle (especially onPause/onStop/onDestroy) is for. No matter what you do, do not put a "quit" or "exit" application button. It is useless with Android's application model. This is also contrary to how core applications work.

Maybe my understanding (and the above quote) are outdated.  It's really not something that I've been keeping up on lately.