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Home » Evaluate \( R(2) \): - Dachbleche24

Evaluate \( R(2) \): - Dachbleche24

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 #### 132.29

📌 A startup’s revenue grows according to the function R(t) = 5000(1.12)^t, where t is time in months. How many months will it take for revenue to exceed $20,000?

📌 Set 5000 × (1.12)^t > 20,000 → (1.12)^t > 4

📌 Take log: t × log(1.12) > log(4) → t > log(4)/log(1.12) ≈ 0.60206 / 0.04922 ≈ 12.23

📌 Since t must be integer, t = 13 months

📌 A student builds a drone that ascends vertically at 4 m/s while expanding a rectangular grid of sensors covering a volume of 1,440 m³ per minute. If the grid width increases at 2 m/s and height at 3 m/s, what is the current width of the grid?

📌 Volume flow rate: dV/dt = area × velocity in depth × rate of expansion? But assume sensor grid expands uniformly in width and height at constant rates.

📌 Let width = w, height = h, length = l. Given: dl/dt = 4 m/s, dh/dt = 3 m/s, width increases at 2 m/s ⇒ dw/dt = 2

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