Question

suppose the percent of households y with internet subscription from the years 2016 to 2019 can be approximated by the linear equation y = 2.22x + 73.80, where x is the number of years after 2010.
a. use this equation or a graph of it to complete the ordered pair (8, ).
b. write a sentence explaining the meaning of the answer found in part (a).
c. if this trend continues, predict the percent of households with an internet subscription in 2023?
d. explain any issues with your answer to part c.
a. complete the ordered pair (8, 91.56)
b. complete the sentence below.
in 2018, approximately 91.56% of households had an internet subscription.
c. complete the sentence below.
in the year 2023, □% of households will have an internet subscription.

Explanation:

Step1: Calculate the value of \(x\) for 2018

The year 2018 is \(2018 - 2010=8\) years after 2010. So \(x = 8\).
Substitute \(x = 8\) into the equation \(y=2.22x + 73.80\).

$$y=2.22\times8+73.80$$

$$y = 17.76+73.80$$

$$y=91.56$$

Step2: Calculate the value of \(x\) for 2023

The year 2023 is \(2023 - 2010 = 13\) years after 2010. So \(x = 13\).
Substitute \(x = 13\) into the equation \(y=2.22x+73.80\).

$$y=2.22\times13 + 73.80$$

$$y=28.86+73.80$$

$$y = 102.66$$

Answer:

a. \((8,91.56)\)
b. In 2018, approximately \(91.56\%\) of households had an Internet subscription.
c. \(102.66\)
d. One issue could be that the linear model assumes a constant rate of increase indefinitely. In reality, there could be saturation (a maximum percentage of households that can have Internet subscriptions) or external factors (such as economic downturns, changes in technology availability) that could affect the growth rate and make the linear prediction less accurate for years far into the future.