27.03.2023 - 15:35

The table shows the average monthly cost C of basic cable television from 2000 through 2008, where t represents the year, with t = 0 corresponding to 2000. a) Use the regression feature of a graphing utility to find a linear model for the data. b) Use t

The table shows the average monthly cost C of basic cable television from 2000 through 2008, where t represents the year, with t = 0 corresponding to 2000.

a) Use the regression feature of a graphing utility to find a linear model for the data.

b) Use the model to estimate the year in which the average monthly cost reached $50.

(Source: SNL Kagan)

{eq}qquad begin{array}{|c|c|} hline & bf color{blue}{\text{ Average}} \ & bf color{blue}{\text{ monthly cost,}, it C} \ bf color{blue}{\text{ Year}} & bf color{blue}{\text{ (in dollars)}} \ hline 0 & 30.37 \ 1 & 32.87 \ 2 & 34.71 \ 3 & 36.59 \ 4 & 38.14 \ 5 & 39.63 \ 6 & 41.17 \ 7 & 42.72 \ 8 & 44.28 \ hline end{array} , {/eq}

Answers (2)
  • bob89rus
    April 3, 2023 в 03:27

    a) Using the regression feature of a graphing utility to find a linear model for the data, we obtain the equation:

    C = 1.61t + 30.37

    Where C is the average monthly cost of basic cable television and t is the year, with t = 0 corresponding to 2000.

    To find this equation, we input the data into the regression feature of a graphing utility, which calculates the best-fit line for the data. In this case, the best-fit line is a linear equation.

    b) We can use the linear equation obtained in part (a) to estimate the year in which the average monthly cost reached $50.

    To do this, we set C = 50 in the equation and solve for t:

    50 = 1.61t + 30.37

    19.63 = 1.61t

    t ≈ 12.19

    Therefore, the average monthly cost of basic cable television reached $50 in the year t = 12.19, which corresponds to the year 2012. However, since t is measured in years after 2000, we need to add 2000 to get the actual year, which gives us the estimate of 2012.

  • bob89rus
    April 9, 2023 в 08:55

    a) Using the regression feature of a graphing utility to find a linear model for the data, we obtain the equation:

    C = 1.61t + 30.37

    Where C is the average monthly cost of basic cable television and t is the year, with t = 0 corresponding to 2000.

    To find this equation, we input the data into the regression feature of a graphing utility, which calculates the best-fit line for the data. In this case, the best-fit line is a linear equation.

    b) We can use the linear equation obtained in part (a) to estimate the year in which the average monthly cost reached $50.

    To do this, we set C = 50 in the equation and solve for t:

    50 = 1.61t + 30.37

    19.63 = 1.61t

    t ≈ 12.19

    Therefore, the average monthly cost of basic cable television reached $50 in the year t = 12.19, which corresponds to the year 2012. However, since t is measured in years after 2000, we need to add 2000 to get the actual year, which gives us the estimate of 2012.

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