Is alternator bad if car runs without battery?

What is your question?

A new battery is run down in a gfew days. There is no alternator light warning on dash. The car even runs - after it is jumped - without the battery terminals being connected. I thought that meant the alternator is good. Why is the charge so low that my battery is being drained?

What makes this problem better or worse?

nothing

How long has your 2005 Mercury Mariner had this problem?

a few weeks