Respuesta :
Solving the quadratic function, the sales are of 9 million in the years of 2000 and 2012.
What is a quadratic function?
A quadratic function is given according to the following rule:
[tex]y = ax^2 + bx + c[/tex]
The solutions are:
[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex]
[tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]
In which:
[tex]\Delta = b^2 - 4ac[/tex]
The number of sales(in millions of dollars), in t years after 2000, is modeled by the following function:
[tex]S(t) = \frac{20t^2 + 800t + 300}{8t^2 + 10t + 100}[/tex]
The sales are of 9 million when S(t) = 9, hence:
[tex]S(t) = \frac{20t^2 + 800t + 300}{8t^2 + 10t + 100}[/tex]
[tex]9 = \frac{20t^2 + 800t + 300}{8t^2 + 10t + 100}[/tex]
[tex]72t^2 + 90t + 900 = 20t^2 + 800t + 300[/tex]
[tex]52t^2 - 710t + 600 = 0[/tex]
Which is a quadratic equation with coefficients a = 52, b = -710, c = 600, hence:
[tex]\Delta = (-710)^2 - 4(52)(600) = 379300[/tex]
[tex]x_1 = \frac{710 + \sqrt{379300}}{104} = 12.7[/tex]
[tex]x_2 = \frac{710 - \sqrt{379300}}{104} = 0.91[/tex]
t is measured in years after 2000, the sales are of 9 million in the years of 2000 and 2012.
More can be learned about quadratic functions at https://brainly.com/question/24737967
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