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/ Take log: u × log(0.88) < log(0.6)
Take log: u × log(0.88) < log(0.6)
February 22, 2026
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An AI algorithm reduces image processing time by 12% with each update. If the initial time is 2.5 seconds, after how many updates will processing time drop below 1.5 seconds?
Solve: 2.5 × (0.88)^u < 1.5
Divide: (0.88)^u < 1.5 / 2.5 = <<1.5 / 2.5 = 0.6>>0.6
u > log(0.6) / log(0.88) ≈ (-0.2219) / (-0.1278) ≈ <<0.2219 / 0.1278 ≈ 1.735>>1.735
So u = 2 updates.
Francie starts a side project independently funded by research grants. She receives $300 in month 1, and each month earns 15% more than the previous. How much does she earn in month 6?
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