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A: 750 - Upplift

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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📌 Solve \( 500 \cdot e^{0.4t} > 5000 \) → \( e^{0.4t} > 10 \) → \( 0.4t > \ln(10) \approx 2.3026 \) → \( t > 2.3026 / 0.4 = 5.7565 \).

📌 Intercept at approximately 5.76 hours; so first integer hour is 6.

📌 A VR developer encodes spatial coordinates into cubic units. A virtual room is modeled as a cube with side length equal to the smallest integer greater than \( \sqrt{200} \). What is the volume of the room in cubic units?

📌 \( \sqrt{200} \approx 14.142 \), so side length = 15. Volume = \(15^3 = 3375\).

📌 An angel investor evaluates a biotech firm whose projected revenue follows the quadratic model \( R(x) = -2x^2 + 40x + 100 \), where \( x \) is years after launch. In which year does revenue peak?

📌 Vertex of parabola: \( x = -\frac{b}{2a} = -\frac{40}{2 \cdot (-2)} = \frac{40}{4} = 10 \).

📌 A game designer uses trigonometric scaling to morph a cube into a sphere. If the cube’s edge length is 6 units, by what factor must the surface area be scaled to match the sphere’s surface area?

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