What to do with my my iphone5s?

Just bought an iPhone5s (plan for 2 years), so normally when I buy a new phone I wait for the battery to get to 0 then fully charge it. So that's what I did with this phone. Then not even 24hours later, it's on 0% again. Now, there's no much signal from where I live unless I go outside the house like at the garage so I put it on airplane mode after charging it to 100%. And use Wi-Fi every now and then when I have to. When I'm using it, it's not really that fast to drain like every after 5mins or so before the batt% goes down. But when I use Wi-Fi, it goes down like every 2 mins.

Is this normal considering that I don't have signal (then put it on airplane mode and use Wi-Fi) or no. Cause it says on apple that:
Talk time: Up to 10 hours on 3G
Standby time: Up to 250 hours
Internet use: Up to 8 hours on 3G, up to 10 hours on LTE, up to 10 hours on Wi-Fi
Video playback: Up to 10 hours
Audio playback: Up to 40 hours

and mine does not even last for 24 hours. Like wtf. Can i ask my carrier(or apple) to replace it?

Yes it's normal. Wi-Fi and LTE use a lot of juice cause it sends a signal. If you want your iphone to last greater than 24 hours. Turn off Wi-Fi when not in use, deactivate all notifications, reduce screen brightness to 50%, Turn off alarms. Turning airplane mode is good if you are not expecting a call or a text messages. And I humbly suggest you buy a powerbank if you are on a hurry.