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The median player salary for the Dallas Cowboys was $441,300 in 2000 and $1,326,720 in 2008. Write a linear equation giving the median salary y in terms of the year x. Then use the equation to predict the median salary in 2016.

Verified Answer :

SociometricStar

Answer:

Linear function is \(y=\frac{221355}{2}x+441300\)

Median salary in 2016 is $2212140

Step-by-step explanation:

Let t = 0 is corresponds to the year 2000.

Thus, basis the given information, we have two points

(0,441300) and (8,1326720)

Slope of the linear function can be found by the formula

\(m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{1326720-441300}{8-0}\\\\m=\frac{221355}{2}​\)

Now, using the point slope form, we can find the linear function

\(y-y_1=m(x-x_1)\\\\y-441300=\frac{221355}{2}(x-0)\\\\y=\frac{221355}{2}x+441300\)

Median salary in 2016 is

\(y=\frac{221355}{2}\times16+441300\\\\y=2212140\)

Building an linear equation, it is found that:

  • The linear equation is \(y = 110677.5x + 441300\)
  • The prediction for the median salary in 2016 is of $2,212,140.

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A linear equation is given by:

@@MATH_TOKEN_1@@

In which m is the slope and b is the y-intercept(which is the value of y when x = 0).

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In this context, the median player salary for the Dallas Cowboys in x years after 2000 is given by:

@@MATH_TOKEN_2@@

In which s(0) is the median player salary in 2000.

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Median salary of $441,300 in 2000 means that \(s(0) = 441300\), and thus:

\(y = mx + 441300\)

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We have two points:

  • (0,441300)
  • (2008-2000, 1326720) = (8,1326720)
  • The slope is given by the change in y divided by the change in x.
  • Change in y: 1326720 - 441300 = 885420
  • Change in x: 8 - 0 = 8.
  • The slope is:

\(m = \frac{885420}{8} = 110677.5\)

Thus, the linear equation is:

\(y = 110677.5x + 441300\)

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2016 is 2016 - 2000 = 16 years after 2000, thus we have to find y when x = 16.

\(y(16) = 110677.5\times16 + 441300 = 2212140\)

The prediction for the median salary in 2016 is of $2,212,140.

A similar question is given at https://brainly.com/question/21504631

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