Even though your battery says charged it may not be 100%. When it hits 100% or thereabouts, it actually discharges a bit, before topping off again. It does this to extend the life of the battery itself. So when you unplug you could be closer to 90%. I don't recommend this at all, but if you don't care about the life of your battery, you can unplug it and plug it back in a few minutes before leaving to top it back off to basically guarantee you are closer to 100%. Doing this can potentially hurt the battery, and have an impact on the daily battery life as the battery may not hold a charge as well.
I would think that is a part of your 87% problem, perhaps it was in the lower 90s when you really started using it. Dropping 5% in an hour or so with some usage, especially if you use 4G, have things updating, screen brightness up....among many other things wouldn't be unheard of.
Battery life is such a tricky thing to pinpoint on what the problem is without a lot more information. Different usage patterns, different app combinations, different locations for different reception strengths, different settings within apps and the OS itself, among other things all can have an impact on your battery life, positively or negatively. I would recommend you look into what is draining your battery, and trying to figure out why if you don't already know, and potentially lower it's drain if possible.
https://play.google.com/store/apps/details?id=com.gsamlabs.bbm <-- GSAM BM is a great tool to help you find the problem points. Lowering the brightness, disabling radios, lowering the amount of times an app synchronizes (or disabling sync completely), and many other things can be done. Perhaps you have a problematic app, that is just unnecessarily draining the battery (I have heard bad things about the Android Facebook app for example).
