Choice A is the correct answer. Use the initial condition to find $A$.

1. At $t=0$: $5000 = \frac{50000}{1 + Ae^0} = \frac{50000}{1 + A}$.
2. Multiply: $5000(1 + A) = 50000$.
3. Divide: $1 + A = 10$.
4. Solve: $A = 9$.
5. Verify: $P(0) = \frac{50000}{1 + 9} = 5000$ ✓

💡 Strategic Tip: Initial condition gives $P_0 = \frac{K}{1+A}$, so $A = \frac{K}{P_0} - 1$.

Choice B is incorrect because this would give $P(0) = \frac{50000}{11} \approx 4545$. Choice C is incorrect because this would give $P(0) = \frac{50000}{6} \approx 8333$. Choice D is incorrect because this would give $P(0) = \frac{50000}{46} \approx 1087$.