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A custom electric motorcycle’s battery degrades by 2.5% of its capacity each year. If the initial range is 120 km, what is the range after 4 years, assuming linear degradation?
Annual degradation: 2.5% of 120 = 0.025 × 120 = <<0.025*120=3>>3 km
Over 4 years: 4 × 3 = <<4*3=12>>12 km
Final range: 120 – 12 = <<120-12=108>>108 km
#108
A historian finds that the number of scientific instruments described in 17th-century texts grew exponentially, doubling every 20 years. If 120 instruments were documented in 1620, how many were documented by 1690?
Number of doubling periods: (1690 – 1620) / 20 = 70 / 20 = 3.5
Growth factor: 2^3.5 = 2^3 × √2 = 8 × 1.4142 ≈ 11.3136
Final count: 120 × 11.3136 ≈ <<120*11.3136=1357.632>>1357.632 → round to 1358
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