Why wouldn't the user just hit the home button? Then they can exit your app from any of your activities, not just a specific one.
If you are worried about your application continuing to do something in the background. Make sure to stop it in the relevant onPause and onStop commands (which will get triggered when the user presses Home).
If your issue is that you want the next time the user clicks on your app for it to start back at the beginning, I recommend putting some kind of menu item or UI button on the screen that takes the user back to the starting activity of your app. Like the twitter bird in the official twitter app, etc.