First off, do a HARD reset on the phone and try the same experiment.
With the phone on, hold down the home button for a second, then while still holding the home button, hold down the power button as well for about 5-10 seconds, until the phone reboots to the apple logo and release. Now charge up your phone to 100%, and run the same experiment.
Also, did you actually SHUT DOWN all the apps running in the background?
To do this, double click the home button to make the recently used apps screen pop up at the bottom of the screen. Long press on one of these apps and they will all start shaking (just like moving apps around on the home screen), but in when they are in that pop up window, you can click the red X on them and all the apps that are "open" in the background will scroll. Close them all until that bottom screen is empty. (don't worry, you aren't actually deleting the apps like you would be on the main page, you're just shutting the apps down).
If, after you've done these simple things, your phone is still draining too quickly I'd start the complaining process and see if you can get it replaced. Especially if the phone is getting "hot" near the rear camera. Those things can go bad, and start heating up, consequently draining the battery very quickly. The batteries themselves rarely go bad. You might want to also check and see if your phone has any tripped liquid sensors...