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Home » Use the formula for the sum of an infinite series: \(S = \fraca1 - r\). - Londonproperty

Use the formula for the sum of an infinite series: \(S = \fraca1 - r\). - Londonproperty

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 \frac{dC}{dt} = -10/(t+2)^2 = -1 \Rightarrow (t+2)^2 = 10 \Rightarrow t = \sqrt{10} - 2 \approx 1.16

📌 \text{No match.}

📌 But perhaps the question meant: when does \( C(t) = 1 \)? Then \( 10/(t+2) = 1 \Rightarrow t = 8 \). Not matching.

📌 Or when does it drop to e-approx 0.25? Then \( 10/(t+2) = 2.5 \Rightarrow t+2 = 4 \Rightarrow t = 2 \).

📌 At \( t = 2 \), \( C'(t) = -10/16 = -0.625 \).

📌 But \( C(t) = 2.5 \) at \( t = 2 \), not 2.5.

📌 Wait — unless the rate is -2.5? No.

📌 Perhaps the function is \( C(t) = \frac{20}{t+2} \)? Then \( C' = -20/(t+2)^2 = -1 \Rightarrow (t+2)^2 = 20 \Rightarrow t = \sqrt{20} - 2 \approx 4.47 - 2 = 2.47 \) — no.

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