How do you know all apps are closed? (hint: not appearing in the Quick Launch ribbon does not mean an app is closed). How long does it take to get to 25%? Do you have an Exchange email account? If so, how many messages are in your inBox, how many contacts, and how many calendar entries do you have in the respective apps? Do you play multiplayer games? Do you have the Facebook app? Do you have news apps (AP, NY Times, WSJ, etc)? Do you have Twitter? What about Yahoo Messenger? Google+? Other apps that show up in the Notifications list in Settings?
This has just started within the past week it seems.
It only took two hours to get to about 25%. As i type now t is RED, and I unplugged almost exactly four hours ago.
For mail I have one Exchange and two GMail accounts, and I just notice something interesting. When I am looking at "Mailboxes" I see that it is CONSTANTLY searching for new mail. Might that be the problem? If so, how do I change to say every five minutes.
I have maybe 150 e-mails, about 500 contacts, and I only use the exchange calendar.
No multiplayer games. No on Facebook, yes on Twitter. I just have Linked In, Weather Channel, Iheart Radio and Pandora
To close the Apps, i pressed the button twice, and all active apps appeared. I then pressed safari and held it, and all active apps appeared in "wiggle mode" and closed everything, except mail.
That's clearly not normal. But your observation about mail is important; the mail app may be stuck. First, press HOME twice and kill mail, like you did the other apps. The reboot the phone by holding HOME and SLEEP until the Apple logo appears (10-20 seconds). Then launch mail and see if it is still constantly updating. If it is go to Settings and turn off the mail account, open mail briefly, then reboot again. Then turn mail back on. If it's an Exchange account turn off Contacts and Calendar also, and launch each of those apps briefly before rebooting.
This should fix it. Normally I would suspect heart radio and pandora, but if you killed them they are not the problem.