In 2000, the average monthly price for basic cable television in the United States was $29.99. In 2016, the average monthly price for the sa

Question

In 2000, the average monthly price for basic cable television in the United States was $29.99. In 2016, the average monthly price for the same basic cable television was $59.75. Write a linear function that models the cost of basic cable television in the United States for x years after 2000. Use the linear function to determine the cost of basic cable television in the United States in the year 2020.

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Ximena 2 weeks 2021-11-18T03:22:13+00:00 1 Answer 0 views 0

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    2021-11-18T03:23:58+00:00

    Answer:

    y(x) = 29.99 + 1.86x

    The cost of basic cable television in the United States in the year 2020 will be $67.19.

    Step-by-step explanation:

    The linear function has the following format.

    y(x) = y(0) + ax

    In which y(x) is the cost x years after 2000, y(0) is the initial cost, that is, the cost in 2000, and a is the slope(how much the cost changes in a year).

    In 2000, the average monthly price for basic cable television in the United States was $29.99.

    This means that y(0) = 29.99

    In 2016, the average monthly price for the same basic cable television was $59.75.

    2016 is 16 years after 2000. So

    y(16) = 59.75

    Write a linear function that models the cost of basic cable television in the United States for x years after 2000.

    y(x) = y(0) + ax

    Applying y(16).

    59.75 = 29.99 + 16a

    16a = 29.76

    a = \frac{29.76}{16}

    a = 1.86

    So

    y(x) = 29.99 + 1.86x

    Use the linear function to determine the cost of basic cable television in the United States in the year 2020.

    2020 is 20 years after 2000, so this is y(20).

    y(x) = 29.99 + 1.86x

    y(20) = 29.99 + 1.86*20 = 67.19

    The cost of basic cable television in the United States in the year 2020 will be $67.19.

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