New iPhone 4s battery problems

I bought an iPhone 4s a month ago. I don't email, I always close the apps right away, my back-light is at a low setting, and I try to drain the battery as much as possible, for a full charge. From the time I go to school, until I get home, my battery only drops to 96% or so. Today, my phone was at 83% at lunch, without use, and 77% at 3pm, when I left school. I checked and there was no apparent app still running. Is there any possible reason this is happening and how can I solve it? My phone is only a month old, I have been trying to use it carefully.

If you still have a warranty than take it back but if you want you can just buy a new battery on ebay their only like 10 dollars and their really easy to replace but it will take your warranty away.

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