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Home » This is a geometric series: a = 8, r = 1.25, n = 5 - Get link 4share

This is a geometric series: a = 8, r = 1.25, n = 5 - Get link 4share

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 New width: \( 6 - (-6) = 12 \) mm

📌 A watershed's water retention capacity is modeled as decreasing linearly by 120,000 m³ per year due to land development. If the current capacity is 8.4 million m³, in how many years will it drop below 6 million m³?

📌 Let \( t \) be years. Capacity = \( 8,400,000 - 120,000t \)

📌 Set: \( 8,400,000 - 120,000t < 6,000,000 \)

📌 Subtract: \( 2,400,000 < 120,000t \)

📌 Divide: \( t > 2,400,000 / 120,000 = 20 \)

📌 So after 21 years, it drops below. But the question asks when it *drops below* — first time ≥ 6M is at t=20, so below at t > 20 → first full year is 21, but "in how many years" means smallest integer t such that condition holds → t = 21

📌 But numerically: \( t = 20 \) gives exactly 6M → needs to go below, so t = 21

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