Yes, you probably need a new alternator.
The alternator is similar to a generator - while the car is running, the alternator is powered by the engine, and constantly recharges the battery. If you're alternator fails, then jumping the battery will provide enough power to start the car, but it will soon die as the battery isn't being charged.
Also, once you get a new alternator, have your battery tested to make sure it still functions properly (letting the battery become depleted may have damaged it).
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