Answer:
a. The approximated salary cap in 2009 is $136.0 millions
b. The salary cap reached 65 million dollars in 2000
Step-by-step explanation:
* Lets explain how to solve the problem
- The quadratic model of the salary cap in million is
y = 0.2313 x² + 2.600 x + 35.17
- The approximation of this cap in millions of dollars for the years
1993-2013 where x = 0 represents 1993, x = 1 represents 1994,
and so on
a. Lets calculate the approximated sports league salary cap in 2009
∵ x at 2009 = 2009 - 1993 = 16
∵ y = 0.2313 x² + 2.600 x + 35.17
∴ y = 0.2313 (16)² + 2.600 (16) + 35.17
∴ y = 135.98 ≅ 136.0 millions
* The approximated salary cap in 2009 is $136.0 millions
b. Lets calculate in what year did the salary cap reach 65 million dollars
∵ y = 65
∵ y = 0.2313 x² + 2.600 x + 35.17
∴ 65 = 0.2313 x² + 2.600 x + 35.17
- Subtract 65 from both sides
∴ 0.2313 x² + 2.600 x - 29.83 = 0
- Use the calculator to find the value of x by solving the quadratic
equation
∴ x = 7.05 and x = -18.29 (we will reject this value)
∴ x ≅ 7 years
∴ The salary cap reached 65 million dollars in (1993 + 7) = 2000
* The salary cap reached 65 million dollars in 2000
