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Home » We begin by factoring both the numerator and the denominator: - High Altitude Science

We begin by factoring both the numerator and the denominator: - High Altitude Science

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 = -4 + 8 + m

📌 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:

📌 For $ t = 1 $: $ a(1)^2 + b(1) + c = 500 \Rightarrow a + b + c = 500 $ (1)

📌 For $ t = 2 $: $ 4a + 2b + c = 1200 $ (2)

📌 For $ t = 3 $: $ 9a + 3b + c = 2100 $ (3)

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\binom{7}{3} \cdot 0^3 \cdot (1 - 0)^4 = 0
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