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Home » These are \( 28 \cdot 1, 28 \cdot 2, 28 \cdot 3 \), so there are 3 such numbers. - Tacotoon

These are \( 28 \cdot 1, 28 \cdot 2, 28 \cdot 3 \), so there are 3 such numbers. - Tacotoon

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 A science policy analyst models the spread of misinformation: it starts with 100 false posts and grows by 40% daily. A public alert system, launched on day 0, reduces the daily growth rate by 15 percentage points each day (starting day 1: 40% → 25% → 10% → ...). On which day does the daily increase drop below 1%?

📌 Growth rate on day n (n ≥ 1): 40% - 15(n−1)%

📌 Set 40 − 15(n−1) < 1 → 40 − 15n + 15 < 1 → 55 − 15n < 1 → −15n < −54 → n > 54/15 = <<54/15=3.6>>3.6

📌 So on day 4, growth rate drops below 1%.

📌 A robotics engineer programs a drone to ascend 3 meters in the first second, then 95% of the previous second’s height each subsequent second. What is the total height, in meters, the drone reaches after 10 seconds, rounded to the nearest tenth?

📌 This is a geometric series: first term a = 3, ratio r = 0.95, n = 10 terms.

📌 Sum = a(1 − r^n)/(1 − r) = 3×(1 − 0.95^10)/(1 − 0.95)

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