Battery Light Question

My battery light stays on for a second or two after I start my car in the morning. I checked the battery and it's about 12.5 volts and I also checked my alternator at the battery and it's cranking out about 14.5 volts. Not sure if the battery is slowly dying, it's about three years old, or if my alternator is starting to die. Anyway, thought I'd post a question and see what might be the problem. I also did searches on it and noticed that most of the threads on alternator problems the battery light stayed on so I haven't gotten to that point yet. Thanks in advance.