Dead alternator?

i think my alternator is dead in my car, the other day i tried to start my car and the battery was dead, i had someone give me a jump start, now i just tried to start it and it wont start again. What is the normal lifetime of an alternator? I have a 2000 dodge durango 5.9 with 160,000 miles on it? thats old enough and enough miles for the alternator to die right?