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Home » r^2 = \frac1503\pi = \frac50\pi - High Altitude Science

r^2 = \frac1503\pi = \frac50\pi - High Altitude Science

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 Question: A materials scientist in Brazil is developing a bio-based plastic that degrades at a rate proportional to the square of the time in weeks, $ t^2 $. The degradation function is modeled as $ D(t) = kt^2 + 5t $, where $ k $ is a constant. If after 3 weeks, the degradation is measured at 48 grams, what is the value of $ k $?

📌 Solution: We are given $ D(t) = kt^2 + 5t $ and that $ D(3) = 48 $. Substituting $ t = 3 $:

📌 = k(3)^2 + 5(3)

📌 Subtract 15 from both sides:

📌 k = \frac{33}{9} = \frac{11}{3}

📌 Thus, the value of $ k $ is $ \boxed{\frac{11}{3}} $.

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