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Home » From Backyard ATP to Party Fun—Revealing the Ultimate Bag Toss Board Dimensions! - Abbey Badges

From Backyard ATP to Party Fun—Revealing the Ultimate Bag Toss Board Dimensions! - Abbey Badges

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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Tₐ = 20°C, T₀ = 95°C, T(10) = 70°C.
= 20 + (95 − 20)e^(−10k) → 50 = 75e^(−10k) → e^(−10k) = 50/75 = 2/3.
Take ln: −10k = ln(2/3) ≈ ln(0.6667) ≈ −0.4055 → k ≈ 0.04055.
Now T(20) = 20 + 75e^(−0.04055×20) = 20 + 75e^(−0.811) ≈ 20 + 75×0.444...
#### 53.34
A research assistant analyzes protein expression data and finds that G...
Model: P(t) = P₀e^(rt).
At t=2, P=120; t=5, P=960.
So: 960 = 120e^(3r) → 8 = e^(3r) → ln(8) = 3r → r = ln(8)/3 = 3ln(2)/3...
But express multiplier per hour: e^r ≈ e^0.6931 ≈ <<exp(0.6931)=2>>2.

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