I can't see your usage stats in that screen shot. Regardless, I can see from your app usage that you should be getting way more than 'a few hours' so try restoring iOS. Something is obviously wrong.
Well, it's basically
13% safari
11% home s
10% music
9% settings
8% messages
Snappseed (that I used to edit 3 pictures since I got the app) 7%
I only got the phone yesterday, will return/exchange tomorrow before work.