not sure of electrical problem

[grmreapr]

Well I put in a brand new battery today. Started fine and everything checked the volts it was 13.4. Started driving and the slowly started to go down im now at 12.8 and it get's worse if I put it in reverse or turn my lights on. My battery light is not on and it's raining out right now so I can't check if my alternator is starting to go. Would anything else be causing these issues besides my alternator Just wondering since I don't have time to check it right now. By the way I have an rb20