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Home » Formula:** \( \left(\frac1.81.2\right)^\frac13 - 1 \) - Veritas Home Health

Formula:** \( \left(\frac1.81.2\right)^\frac13 - 1 \) - Veritas Home Health

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 5Question: Find the time $ t $ at which the growth rates of two marine species, modeled by $ 3^{t} $ and $ 9^{t-1} $, are equal.

📌 Solution: Set $ 3^{t} = 9^{t-1} $. Since $ 9 = 3^{2} $, rewrite the equation as $ 3^{t} = (3^{2})^{t-1} $. Simplify the right-hand side: $ 3^{t} = 3^{2(t-1)} $. Equate the exponents: $ t = 2(t - 1) $. Solve: $ t = 2t - 2 $, so $ t = 2 $. Verify by substituting back: $ 3^{2} = 9^{1} $ → $ 9 = 9 $. Thus, the time is $ \boxed{2} $.

📌 Question: A community biotech researcher mixes two solutions: one with 15% vinegar and another with 5% vinegar. How many liters of each are needed to make 20 liters of 10% vinegar?

📌 Solution: Let $ x $ be liters of 15% solution and $ y $ be liters of 5% solution. The system is:

📌 x + y = 20 \\

📌 0.15x + 0.05y = 2 \quad (\text{since } 10\% \text{ of } 20 = 2)

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