#### 74.08

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• Daily distance = 15 × 8 = 120 km. Total distance = 120 × 21 = 2520 km.
• An environmental scientist models air quality with the equation C = C₀e^(-kt). If C₀ = 100 µg/m³, k = 0.1/year, and t = 3 years, what is C?
• C = 100 × e^(-0.1×3) ≈ 100 × e^(-0.3) ≈ 100 × 0.7408 ≈ 74.08 µg/m³.
• An archaeologist dates a pottery shard using carbon-14, which has a half-life of 5730 years. If 25% of the original carbon-14 remains, how old is the shard?
• Using N = N₀(0.5)^(t/5730), 0.25 = (0.5)^(t/5730). Solving: t = 5730 × 2 = 11,460 years.
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