To find the number of infected passengers after one week (7 days), we need to evaluate the function \( A(t) = 3e^{0.35t} \) at \( t = 7 \).
Substituting \( t = 7 \):
\[ A(7) = 3e^{0.35 \times 7} \] \[ A(7) = 3e^{2.45} \]
Now, we calculate \( e^{2.45} \):
Using a calculator, you find that:
\[ e^{2.45} \approx 11.6 \]
Now substitute this value back into the equation:
\[ A(7) \approx 3 \times 11.6 \approx 34.8 \]
Rounding to the nearest whole number, we find:
\[ A(7) \approx 35 \]
Thus, the number of passengers infected after one week is approximately 35 passengers.