toyota electrical problem?

1994 toyota tercel. I was driving to work and car died while making a u-turn. It died and lights and dash were very weak. Could not restart. Got a jump and drove for 100 ft and died again. Charged the battery and started and got me home (35mi) with a stop along the way where I turned the car off and then restarted it. The next day drove another 20 mi to have ac repaired. When i came back to pick the car up it would not start acting like the battery was dead. Got a jump and drove home without incident. Now can jump but have to jump every time I turn the car off. Alternator sounds most likely but want to add another detail. At home I checked the battery voltage with the car off and it read 12.77v and 14.82 when running. Again jump started the car, then disconnected the battery from the car and the car kept running but died the instant i turned on the headlights. Is alternator working but very weak or is there a problem with the battery perhaps?

 

it turns out that the battery needed replacing. thanks anyway