IPhone 5s Rapidly losing battery?

I bought my unlocked iPhone 5s 32GB sometime between October and November (sorry i can't remember the exact time) and recently (within the last month) my iPhone has been noticeably losing battery at a ridiculously fast rate. Today when i went to school i had full battery charge and when i came home i had only 7% left, and i only used my iPhone for about an hour listing to music with the screen off and not web surfing. I also made sure to turn off anything that sends or receives signals (except for data although i didn't use it) and turn down the brightness of the screen about to half way. I'm just wondering if there's anything else i can do to ether fix this problem or minimize it. The phone also seems not to charge as fast anymore and i'm wondering if there could be battery damage. Although i haven't dropped the phone or damaged it in any way. I have already looked up this question on the internet and i have tried everything they have recommended but it hasn't helped so far. Any ideas would be much appreciated!

I would just take it to an apple store, they will probably just put a new battery in for free if what you say is really true. Most often people complain they used it for just an hour but in reallity used it 5.

I know a few people that have given up their iPhones for that very reason. According to them the latest OS drained their batteries much faster than they were used to.
(They're all happy with their new phones!)

Apparently the iphone isn't that old all apple product has a 1 year limited warranty go to apple store or send it to apple to get a replacement.