2004 Honda Accord alternator or battery?

Electrical problem
2004 Honda Accord Front Wheel Drive Automatic 141000 miles

the accord has a battery idiot light. It has come on intermittently, been checked but cannot find out why. Yesterday it came on and later in the day the car would not start. We were able to jump it started but the lights remained dim and revving the engine did not change anything. I thought if you revved the engine, the lights would get brighter. But they did not and battery died again. That leads me to believe the alternator is not providing electricity to the components and charging the battery.