The apps on my Android are constantly running and draining my battery. I downloaded the NQ Android Booster help with battery life but when I try to stop the apps from running on it, it only really suspends them until I am out of the booster section, then the apps turn right back on. Is anyone else having this problem and how do I fix it?

In general, applications won't need an "Exit" Button inside Andorid OS. There is a lifecylce for every application where you have certain automatic exit and return or reentry points. This is, onPause, onStop, onDestroy and so on.

If an application is done well, there is no need for an explicit exit button. If it is prgrammed in a way which differs from best practice, chances high that some routines will stay in memory and the OS will encounter problems removing this app from application stack.

Source: How to stop apps running in background mode????? — Android Forum - AndroidPIT

There is an option on the newer Android Smartphones that is called Power Saving Mode .

Keep this mode on all the time.
Go to setting and Scroll down to power savings mode Swipe to ON position. Check all. Also keep your Brightness on Auto or at the lowest.

The best app around to fix this problem is called Juice Defender in the Google Play Market... Choose Advanced options.
Also, if you buy the full version you will get better battery Saver options.