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Home » Volume of sphere: $\frac43\pi x^3$. - go-checkin.com

Volume of sphere: $\frac43\pi x^3$. - go-checkin.com

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 A virtual reality developer creates a new immersive environment where users can explore a bioluminescent forest. Each tree emits light with an intensity following an exponential decay model: \( I(h) = I_0 \cdot e^{-kh} \), where \( I_0 = 1000 \) lumens is the initial intensity at ground level, and \( k = 0.2 \) per meter. If a user stands 5 meters from a tree, what is the light intensity they experience?

📌 Calculate \( I(5) = 1000 \cdot e^{-0.2 \cdot 5} = 1000 \cdot e^{-1} \approx 1000 \cdot 0.3679 = 367.9 \) lumens.

📌 #### 367.9

📌 An angel investor allocates $2.5 million across 4 biotech startups. She invests 30% in gene-editing, 25% in synthetic biology, 20% in AI-driven drug discovery, and the remainder in regenerative medicine. How much, in dollars, was invested in regenerative medicine?

📌 Total percentage allocated: 30 + 25 + 20 = 75%. Remaining: 100 - 75 = 25%.

📌 Amount: 25% of $2,500,000 = 0.25 × 2,500,000 = 625,000.

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