Choice A is the correct answer. Solve for $t$ when $I(t) = 5000$.

1. Equation: $5000 = \frac{10000}{1 + 9999e^{-1.5t}}$.
2. Multiply: $5000(1 + 9999e^{-1.5t}) = 10000$.
3. Simplify: $1 + 9999e^{-1.5t} = 2$.
4. Isolate: $9999e^{-1.5t} = 1$, so $e^{-1.5t} = \frac{1}{9999}$.
5. Natural log: $-1.5t = \ln(\frac{1}{9999}) = -\ln(9999) \approx -9.21$.
6. Solve: $t = \frac{9.21}{1.5} \approx 6.14 \approx 6.1$ days.

💡 Strategic Tip: In logistic models, half of carrying capacity occurs when $Ae^{-rt} = 1$.

Choice B is incorrect because this is too long. Choice C is incorrect because this is too short. Choice D is incorrect because this is way too long.