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Home » Because You Deserve to Know Every Hidden Cove—Download the Ultimate Caribbean Sea Map! - 500apps

Because You Deserve to Know Every Hidden Cove—Download the Ultimate Caribbean Sea Map! - 500apps

📅 March 13, 2026 👤 scraface

Mar 13, 2026

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📌 ### Frage 5

📌 Ein Umweltingenieur modelliert die Konzentration \( C \) eines Schadstoffs in einem See als \( C(t) = C_0 e^{-kt} \), wobei \( C_0 = 100 \) mg/L, \( k = 0.05 \) Tag\(^{-1}\), und \( t \) in Tagen gemessen wird. Wie lange dauert es, bis die Konzentration unter 10 mg/L fällt?

📌 Stelle die Ungleichung auf: \( 100 e^{-0.05t} < 10 \).

📌 Teile beide Seiten durch 100: \( e^{-0.05t} < 0.1 \).

📌 Nimm den natürlichen Logarithmus: \( -0.05t < \ln(0.1) \).

📌 Da \( \ln(0.1) \approx -2.3026 \), \( -0.05t < -2.3026 \).

📌 Dividiere durch -0.05 (kehre die Ungleichung um): \( t > \frac{2.3026}{0.05} \approx 46.052 \).

📌 #### 46.052

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