In 1996, the sports league introduced a salary cap that limits the amount of money spent on players' salaries. The quadratic model $y=0.2313 x^{2}+2.600 x+35.17$ approximates this cap in millions of dollars for the years $1996-2006$, where $x=0$ represents 1996, $x=1$ represents 1997 , and so on. Complete parts $a$ and $b$.
a. Approximate the sports league salary cap in 2004.
The approximate sports league salary cap in 2004 is $\$ \square$ million. (Round to the nearest tenth as needed.)

Step 1 ：In 1996, the sports league introduced a salary cap that limits the amount of money spent on players' salaries. The quadratic model \(y=0.2313 x^{2}+2.600 x+35.17\) approximates this cap in millions of dollars for the years 1996-2006, where \(x=0\) represents 1996, \(x=1\) represents 1997 , and so on.

Step 2 ：To find the approximate sports league salary cap in 2004, we need to substitute \(x=8\) into the quadratic model, because \(x=0\) represents 1996, so \(x=8\) represents 2004.

Step 3 ：Substituting \(x=8\) into the quadratic model, we get \(y = 0.2313*8^{2} + 2.6*8 + 35.17\)

Step 4 ：Solving the equation, we get \(y = 70.7732000000000\)

Step 5 ：Rounding to the nearest tenth as needed, we get \(y = 70.8\)

Step 6 ：Final Answer: The approximate sports league salary cap in 2004 is \(\boxed{70.8}\) million.