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Home » At t=2, P=120; t=5, P=960. - Leaselab

At t=2, P=120; t=5, P=960. - Leaselab

📅 February 26, 2026 👤 scraface

Feb 26, 2026

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📌 Acceleration doubles every 2 seconds: this is exponential growth: a(t) = a₀ × 2^(t/2)

📌 a₀ = 0.5 m/s², t = 10 s

📌 a(10) = 0.5 × 2^(10/2) = 0.5 × 2^5 = 0.5 × 32 = 16 m/s²

📌 A robotics engineer is programming a robotic assistant to sort medical supplies in a hospital. The robot processes 8 items in the first minute, and each minute thereafter it processes 125% of the previous minute’s count due to optimized AI routing. How many items does it process in total during the first 5 minutes?

📌 This is a geometric series: a = 8, r = 1.25, n = 5

📌 Total items = a(r^n - 1)/(r - 1) = 8(1.25^5 - 1)/(0.25)

📌 1.25^2 = 1.5625

📌 1.25^4 = (1.5625)^2 = 2.44140625

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