While you might have a disposal that is new and strong, if the pipe it drains into is old and particularly if it's galvanized, you should take some special precautions. Specifically, the less food scraps you put into the disposal and the more you put them into the garbage bin the better. Many foods, including even egg shells, get finely ground in the disposal and end up like sand that doesn't just clog the drain, but actually adheres to the drain's walls shrinking its diameter. Also as a best practice, every three days you should fill the sink with warm water and run the disposal until it empties, which is the best prophylactic way to avoid expensive drain pipe replacement, especially if the drain pipe goes into a concrete floor or block wall. If your sink becomes clogged, especially in an old house, you should call an experienced and trusted plumber instead of one of the commercial Roto-Rooter services. Doing so usually will save you money (Roto-Rooter reps work on commission and will tend to do more than is needed at greater cost and will not instruct you in best practices) and get you better service. In Phoenix, your best bet is Tyson Mustain at 623-512-5874.
If you are unfamiliar with what a kitchen sink disposal system looks like, this should help:
If you are unfamiliar with what a clogged kitchen sink looks like, this should help:
If you are unfamiliar with what someone looks like after the plumber unclogs a kitchen sink, this should help: