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Home » Question: A fish population in a polluted lake is modeled by the function - ToelettAPP

Question: A fish population in a polluted lake is modeled by the function - ToelettAPP

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 Let \( R(t) = R_0 \cdot (1/2)^{t/150} \), where \( R_0 \) is the ratio 150 years ago.

📌 But we need the actual ratio today.

📌 Suppose \( t = 0 \) is now.

📌 Let the ratio today (at t=0) be \( R(0) = 1/16 \) (birch:pine).

📌 But 150 years ago, it was higher: \( R(0) / R_{\text{past}} = 1/2 \Rightarrow R_{\text{past}} = 2 \cdot R(0) = 2/16 = 1/8 \)

📌 We want when ratio was 1:1 = 1.

📌 So: $ 1 = \frac{1}{8} \cdot (1/2)^{t/150} $ → no — that’s not correct.

📌 The ratio evolves: if it halves, then:

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