Question

in 1995, the sports league introduced a salary cap that limits the amount of money spent on players salaries. the quadratic model ( y = 0.2313x^{2}+2.600x + 35.17 ) approximates this cap in millions of dollars for the years 1995 - 2006, where ( x = 0 ) represents 1995, ( x = 1 ) represents 1996, 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 ( $ ) million.
(round to the nearest tenth as needed.)

Explanation:

Step1: Determine the value of \(x\) for 2004

Since \(x = 0\) represents 1995, for 2004, \(x=2004 - 1995=9\).

Step2: Substitute \(x = 9\) into the quadratic model \(y = 0.2313x^{2}+2.600x + 35.17\)

$$
LATEXBLOCK0
$$

Step3: Round the result to the nearest tenth

Rounding \(77.3053\) to the nearest tenth, we look at the hundredth - digit. The hundredth - digit is \(0\), so \(y\approx77.3\)

Answer:

\(77.3\)