#### 249.4

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• Planet Z is 4× farther than Y → R_Z = 4 × R_Y → R_Z³ = 64 × R_Y³ = 64 × 27 = <<64*27=1728>>1,728.
• T_Z² = (R_Z³) × (T_Y²)/(R_Y³) = 1,728 × (972 / 27) = 1,728 × 36 = <<1728*36=62208>>62,208.
• T_Z = √62,208 = <<sqrt(62208)=249.4>>≈ 249.4 Earth years.
• A geographer is mapping a region using GIS and finds that the population density increases exponentially from 50 people/km² at 10 km from a city center to 800 people/km² at 20 km. Assuming exponential growth, what is the density at 15 km?
• Model: D(r) = D₀ × e^(kr), where r is distance from center.
• D(10) = 50, D(20) = 800.

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