The function $N(t)=\frac{12,000}{1+999 e^{-t}}$ models the number of people in a small town who have caught the flu $t$ weeks after the initial outbreak. Step 2 of 2 : How many people have caught the flu after 12 weeks? Round to the nearest person.

Step 1 ：Substitute \(t=12\) into the function \(N(t)\) to get \(N(12)=\frac{12,000}{1+999 e^{-12}}\).

Step 2 ：Calculate the value of the exponent: \(e^{-12} \approx 6.14421235332821 \times 10^{-6}\).

Step 3 ：Multiply this value by 999: \(999 \times 6.14421235332821 \times 10^{-6} \approx 0.0061380679409946\).

Step 4 ：Add 1 to this result: \(1 + 0.0061380679409946 \approx 1.0061380679409946\).

Step 5 ：Divide 12,000 by this result: \(\frac{12,000}{1.0061380679409946} \approx 11922.22\).

Step 6 ：Round to the nearest person to get the final answer: \(\boxed{11922}\) people have caught the flu after 12 weeks.