My iPhone 5 has been acting strange recently. First of all, it is a launch day model, so over a year old now. 4 or 5 times it has shut off completely on it's own, as if the battery is dead, but its been at roughly 20%. Last night it did it again, but the battery was at 30%. When I plug it in, and turn it back on, the battery is still at wherever it left off, so last night it still said 30%. Is my battery slowly dieing? If so, anyone happen to know how much it costs to replace the battery at the Apple Store? The problems all started after iOS 7, but I honestly think it is a coincidence. Ideas?