new battery + terminals + good cranking starter, but no juice to start

I have a 2002 subaru forester that does not have enough power to start only a week after replacing the battery + terminals. When jumped, it fires up strong and immediately, leading me to believe that the alternator needs replaced and isn't refilling the battery. The starter motor sounds find and makes no unusual sounds, and works right away. It (the alternator) has not been replaced in the 6 years my wife has owned it. Also, the previous battery did not have enough power or amps according to the mechanic who tested it last week when we diagnosed the bad battery.