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Final count = 500 × 2¹⁵
2¹⁰ = 1024, 2¹⁵ = 1024 × 32 = 32,768
× 32,768 = 16,384,000
#### 16384000
On Mars, a colony’s water recycling system recovers 85% of used water daily. If colonists consume 400 liters per day, how much new water must be imported after 7 days to sustain the colony, assuming no initial reserves?
Each day, 15% of water is lost: 15% of 400 = 0.15 × 400 = 60 liters lost daily
Total loss over 7 days = 60 × 7 = 420 liters
So, 420 liters must be imported after 7 days to maintain supply
An AI specialist trains a model to classify images. The model improves by reducing error rate by half each week. If the initial error rate is 32%, what will it be after 5 weeks?
Error rate halves weekly: geometric sequence with ratio 0.5