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Home » + 26 = 93 \text million miles - Sterling Industries

+ 26 = 93 \text million miles - Sterling Industries

📅 April 16, 2026 👤 scraface

Apr 16, 2026

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📌 Problem:** A car depreciates such that its value after \( t \) years is \( V(t) = 25000(0.85)^t \). After how many years will its value drop below $10,000?

📌 Solve \( 25000(0.85)^t < 10000 \)

📌 Divide: \( (0.85)^t < \frac{10000}{25000} = 0.4 \)

📌 Take logarithm: \( t \ln(0.85) < \ln(0.4) \)

📌 \( t > \frac{\ln(0.4)}{\ln(0.85)} \approx \frac{-0.9163}{-0.1625} \approx 5.64 \)

📌 So, after 6 years, value drops below $10,000.

📌 Problem:** A function \( f(x) = x^3 - 6x^2 + 11x - 6 \) has roots \( r, s, t \). What is \( r^2 + s^2 + t^2 \)?

📌 By Vieta’s formulas:

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