BATTERY / ALTERNATOR PROBLEM?

The battery in my car was in it when I bought it about 8 months ago. I have the receipt from when the battery was bought and it's only 10 months old. Granted, it's a Walmart battery, but it's not very old. The problem is, the fluid level in the battery is constantly depleting itself and if I drive it a few days then let it sit a week or so the battery is dead. With my limited knowledge, I think there is an alternator problem and it's boiling my battery. I say this because this last time after filling the resevoirs, I dried off any spillage and drove it for a while. When I got home I checked and the top of the battery around the fill caps was wet. There is no indication the battery is leaking anywhere else. Any help or info will be greatly appreciated.
 
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