Question

in 1994, the sports league introduced a salary cap that limits the amount of money spent on players salaries. the quadratic model y = 0.2313x²+2.600x + 35.17 approximates the cap in millions of dollars for the years 1994 - 2010, where x = 0 represents 1994, x = 1 represents 1995, and so on. complete parts a and b.
a. approximate the sports league salary cap in 2008.
the approximate sports league salary cap in 2008 is $□ million. (round to the nearest tenth as needed.)

Explanation:

Step1: Determine the value of x for 2008

Since x = 0 represents 1994, for 2008, the number of years from 1994 is 2008 - 1994=14. So x = 14.

Step2: Substitute x into the quadratic - model

We have the quadratic model y = 0.2313x²+2.600x + 35.17. Substitute x = 14 into the equation:
\[

$$\begin{align*} y&=0.2313\times14^{2}+2.600\times14 + 35.17\\ &=0.2313\times196+36.4+35.17\\ &=45.3348+36.4 + 35.17\\ &=45.3348+71.57\\ &=116.9048 \end{align*}$$

\]

Step3: Round to the nearest tenth

Rounding 116.9048 to the nearest tenth gives 116.9.

Answer:

116.9