#### 24.1

February 22, 2026

#### 24.1

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Sum = a(1 − r^n)/(1 − r) = 3×(1 − 0.95^10)/(1 − 0.95)
0.95^10 ≈ 0.5987 → 1 − 0.5987 = 0.4013
Denominator: 0.05 → Sum = 3 × 0.4013 / 0.05 = 3 × 8.026 = <<3*8.026=24.078>>24.078 ≈ 24.1 meters
An experimental chemist develops a catalyst that increases reaction efficiency by 5% of the remaining inefficiency each hour. If the initial inefficiency is 20%, after how many full hours will inefficiency drop below 5%?
Initial inefficiency: 20%. Each hour, 5% of the current inefficiency is reduced. So inefficiency follows:
after 1 hr: 20 × 0.95 = 19

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