During an epidemic, the number of people who have never had the disease and who are not immune (they are susceptible) decreases exponentially according to the following function, where $t$ is time in days. \[ f(t)=17,000 e^{-0.04 t} \] Find the number of susceptible people at each time. (a) at the beginning of the epidemic (b) after 11 days (c) after 2 weeks

Step 1 ：Given the function \(f(t)=17,000 e^{-0.04 t}\), where \(t\) is time in days, we can find the number of susceptible people at different points in time by substituting the given time into the function.

Step 2 ：(a) At the beginning of the epidemic, \(t=0\). Substituting \(t=0\) into the function gives \(f(0)=17,000 e^{-0.04 \times 0} = 17000\). So, at the beginning of the epidemic, the number of susceptible people is \(\boxed{17000}\).

Step 3 ：(b) After 11 days, \(t=11\). Substituting \(t=11\) into the function gives \(f(11)=17,000 e^{-0.04 \times 11} \approx 10948.619158413403\). So, after 11 days, the number of susceptible people is approximately \(\boxed{10949}\).

Step 4 ：(c) After 2 weeks, \(t=14\) (since 1 week = 7 days). Substituting \(t=14\) into the function gives \(f(14)=17,000 e^{-0.04 \times 14} \approx 9710.554085429852\). So, after 2 weeks, the number of susceptible people is approximately \(\boxed{9711}\).