Battery Light/Discharging

My husband's 1999 Chevy S-10 has the battery light on. The gauge is usually up at 14 but is is down at 10 or 12 now. There does not seem to be any loss of power, lights are on and truck is running. The battery is 3 or 4 years old, the alternator came with the truck. As a test, he took the old battery out and put the battery from his other truck into the S-10. That still didn't change anything, the battery light is still on in the S-10 and the gauge is down. What do you think could be causing the light to stay on and the gauge to show battery discharge?

most likely cause is the alternator.