\[ P(t)=\frac{5730}{1+4.73 e^{-0.4 t}} \] a) Find the population after 17 years. (Round to the nearest integer as needed.)

Step 1 ：Given the population function \(P(t)=\frac{5730}{1+4.73 e^{-0.4 t}}\)

Step 2 ：We are asked to find the population after 17 years, so we substitute \(t=17\) into the equation

Step 3 ：After substituting, we get \(P(17) = 5699.971657551409\)

Step 4 ：Rounding to the nearest integer, we get \(P(17) = 5700\)

Step 5 ：Final Answer: The population after 17 years is \(\boxed{5700}\)