Having apps open does not drain the battery and slow the device. Very few apps stay open, even if they appear when you double-click your home button. This just shows the most recently used apps, though music apps like Pandora do continue to run while minimized (if you can still hear the music, it’s running). The biggest drains to your battery life actually come from often you set your phone to fetch mail, how often you use applications (like every time you check Facebook) and how often your apps are set to push notifications to you.