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smart city la 2028 - Simpleprint

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 We solve: \( 1 \times (1.1)^n = 1000 \) → \( (1.1)^n = 1000 \)

📌 Take log: \( n = \log_{1.1}(1000) = \frac{\log 1000}{\log 1.1} = \frac{3}{0.04139} \approx 72.45 \)

📌 So depth: \( 72.45 \times 100 \approx 7245 \) meters (round to nearest 100 m where it exceeds)

📌 At 7200 m: \( (1.1)^{72} \approx 999.9 \) → just below

📌 At 7300 m: \( (1.1)^{73} \approx 1099.9 \) → exceeds

📌 So it reaches 1000 atm during ascent at ~7300 meters. But question asks for depth before reaching — so maximum depth where it's ≤1000.

📌 Since 72.45 × 100 = 7245, check:

📌 \( (1.1)^{72.45} = 1000 \) → depth = 7245 m exceeds, so first depth where it exceeds is 7245 m. But we want when it first reaches or exceeds — so depth = 7245 m. However, for precision in math context without trig, and aligning with format, use:

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