Hello an welcome to the forum. It's not normal that the battery should drop that way, unless you have things runing in the background and thus huging the battery.
Have you setup automatically fetch email? If yes what about the time period of automatically fetching email?
Double press "home button" and you will see the multitasking bar, inthere you will see all the apps you've recentely run, tap and hold on any app there until all if them start wiggling, by then you will see a "minus" sign on top left on each app, tap that minus sign to completely close all the apps.
Finally soft reset your phone by pressing both home button and power button until the device power off it self and power on back and display the apple logo, then release both buttons.
Also make sure that your bat is really full charged and display the full battery charge sign before you unplug it, because your phone will display 100% but it doesn't mean that it's already full charged.
Try those steps and see if it helps.
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