[Accord092]

I know it's a stupid question but should a alternator light come on when i turn my key to the on position in my 89 crx si? If I have one it never lights up. Anyways, I've been having troubles keeping the battery charged and am wondering what's going on. After jump starting it I drove the car for and hour or so and it ran fine, but when i shut it off at the gas station it died. Do you think it was just the battery being old and not holding a charge? I hate electrical problems