Voltometer Reading

[scruffboy]

I put a new battery in my car after the old one apparently died (it was a Sunday and I had my son for the weekend and just bought a new battery to get him to his mother before she threw a fit). I would have liked to have had the old battery checked but couldn't. Anyway, since putting in the new battery, the voltometer usually reads between 12 and 14 (I think the top number is 18). It also moves up when I rev the engine. Is this a good sign that my alternator is working? I don't want to do that old school test of removing the pos wire as my manual says not to and you guys told me I could fry some computer components. So, does it sound like my alternator is working and my battery really just crapped out on me?

Thanks

Scruffboy