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Home » English-only total: \( 40 \times 2.5 = 100 \) - go-checkin.com

English-only total: \( 40 \times 2.5 = 100 \) - go-checkin.com

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 This is a first-order difference equation. The difference $ E(t+1) - E(t) $ is linear in $ t $, so $ E(t) $ must be a quadratic polynomial. Let $ E(t) = at^2 + bt + c $.

📌 From the initial condition:

📌 E(0) = c = 0.

📌 Now compute the difference:

📌 E(t+1) - E(t) = a(t+1)^2 + b(t+1) - (at^2 + bt) = a(2t+1) + b = 2at + (a + b).

📌 Set equal to $ 2t + 1 $:

📌 2at + (a + b) = 2t + 1.

📌 2a = 2 \Rightarrow a = 1, \quad a + b = 1 \Rightarrow 1 + b = 1 \Rightarrow b = 0.

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