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Home » Divide both sides by \(2 imes 3.14159\): - SUpost

Divide both sides by \(2 imes 3.14159\): - SUpost

📅 July 6, 2026 👤 scraface

Jul 06, 2026

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📌 Wait: 5 seasons → 1 initial increase, then 4 growth increments? But:

📌 Type: $ Y_n = Y_{n-1} + r \cdot (\text{prev increase}) $, with pre-increase 100, then 90, 81, etc.

📌 Actually, increase forms a geometric sequence: $ d_1 = 100 $, $ d_2 = 90 = 0.9 \times 100 $, $ d_3 = 81 = 0.9^2 \times 100 $, ..., $ d_k = 100 \times (0.9)^{k-1} $

📌 Total increase over 5 seasons: $ \sum_{k=1}^{4} d_k $ (since first is initial, then 4 more)

📌 But: $ Y_1 = 500 \times 1.2 = 600 $

📌 $ Y_2 = Y_1 + d_1 $, $ Y_3 = Y_2 + d_2 $, ..., $ Y_5 = Y_4 + d_4 $? No — each increase is applied once per season.

📌 Better: The *amount* added in year $ n $ is $ I_n $, where $ I_1 = 100 $, $ I_2 = 0.9 \times 100 = 90 $, $ I_3 = 0.9 \times 90 = 81 $, $ I_4 = 72.9 $, $ I_5 = 65.61 $

📌 Then $ Y_1 = 600 $

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