If you have a volt/ohm meter you can check it yourself. Open the hood and tilt the fuse block on top of the battery out of the way. Put your meter on volts DC and check the battery. Then start the car and while it's running check the battery again. Not running it should be 12+ volts and running it should be in the 13.5-14.2 range. If it doesn't change once it's running, then the alternator has shot craps.