iPhone 5 shuts down at 25% on iOS 7.0.4 My iPhone 5 has been shutting down earlier than normal at lower battery levels. 

First, it started to shut down around 10%, then it increased to 15%, 20%, and finally 25%. I used to be able to run it down to 1%. 

The battery indicator also jumps down sometimes by around 10-15%.

I have only had this problem ever since updating to iOS 7.0.4 (from 7.0.3). I have done multiple iTunes restores since I updated, but the problem still has not been fixed.

Is there a fix for it?
I called Apple about this and they said 2 things:


the numbers provided are approximate 
certain apps in background can be battery hogs. She specifically said that the camera app native to iOS7 continues full battery use in background and they were aware of this. She suggested being careful NOT to keep camera in background (i.e. double tap iOS button and slide camera up to remove from background active list)


This must have been the problem for me because battery life immediately improved. It still shuts down soon after going below 20% but it had been at 25% when I called.