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Understanding the Context

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The value of $ m $ is $ \boxed{8} $.
Question: A science communicator models the growth of a YouTube channel's subscribers with $ S(t) = at^2 + bt + c $. If $ S(1) = 500 $, $ S(2) = 1200 $, and $ S(3) = 2100 $, find $ a $.
Solution: Set up equations using the given points:

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