#### 0.173

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• Given $ t_{1/2} = 4 $ years:
• $ 4 = \frac{\ln(2)}{k} $
• $ k = \frac{\ln(2)}{4} \approx \frac{0.693}{4} = 0.173 $ per year
• A search and rescue robot moves at 2.5 m/s but encounters a 30° incline that reduces its effective speed by 15%. What is its new speed along the slope?
• The speed reduction is $ 2.5 \times 0.15 = 0.375 $ m/s.
• New speed = $ 2.5 - 0.375 = 2.125 $ m/s

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