Home / Divide both sides: 2 > 1 + 99e^(−0.5t) → 1 > 99e^(−0.5t) → e^(−0.5t) < 1/99

Divide both sides: 2 > 1 + 99e^(−0.5t) → 1 > 99e^(−0.5t) → e^(−0.5t) < 1/99

February 22, 2026

#### 420
Rick models the spread of a virus in a community of 10,000 people. The model uses the logistic function P(t) = 10000 / (1 + 99e^(−0.5t)), where P(t) is the number infected after t days. After how many full days will more than 5,000 people be infected?
Solve: 10000 / (1 + 99e^(−0.5t)) > 5000
Take natural log: −0.5t < ln(1/99) = −ln(99) ≈ −4.595
Multiply by −2 (reverse inequality): t > 4.595 × 2 = <<4.595*2=9.19>>9.19
So, after 10 full days.