I'm on an iphone 6s and haven't had any issues with battery life. I know some have been experiencing battery drainage since upgrading to iOS10 but had you already begun to experience any battery issues before upgrading? When my sister still had her iphone 5s, after about a year and a half her battery just did not work as it used to no matter was iOS she was on. And it would shut off even though the phone showed her having 30-35%. Pretty much the same symptoms your phone is having.