Respuesta :
Answer:
[tex]y(x) = 29.99 + 1.86x[/tex]
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.
[tex]y(x) = y(0) + ax[/tex]
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 [tex]y(0) = 29.99[/tex]
In 2016, the average monthly price for the same basic cable television was $59.75.
2016 is 16 years after 2000. So
[tex]y(16) = 59.75[/tex]
Write a linear function that models the cost of basic cable television in the United States for x years after 2000.
[tex]y(x) = y(0) + ax[/tex]
Applying y(16).
[tex]59.75 = 29.99 + 16a[/tex]
[tex]16a = 29.76[/tex]
[tex]a = \frac{29.76}{16}[/tex]
[tex]a = 1.86[/tex]
So
[tex]y(x) = 29.99 + 1.86x[/tex]
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).
[tex]y(x) = 29.99 + 1.86x[/tex]
[tex]y(20) = 29.99 + 1.86*20 = 67.19[/tex]
The cost of basic cable television in the United States in the year 2020 will be $67.19.
