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.

Answer 1

`y(x) = 29.99 + 1.86x`

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

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 = (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.