Question

suppose the percent of households y with internet subscription from the years 2016 to 2019 can be approximated by the linear equation y = 2.13x + 72.30, where x is the number of years after 2010.
a. use this equation or a graph of it to complete the ordered pair (9, ).
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 2024?
d. explain any issues with your answer to part c.
a. complete the ordered pair
(9 94.98)

Explanation:

Step1: Substitute x - value

Given the linear equation $y = 2.13x+72.30$ and $x = 9$. Substitute $x = 9$ into the equation:
$y=2.13\times9 + 72.30$

Step2: Calculate the product

$2.13\times9=19.17$
So, $y = 19.17+72.30$

Step3: Calculate the sum

$y=19.17 + 72.30=91.47$

Step4: Interpret the ordered - pair

The ordered pair $(9,91.47)$ means that 9 years after 2010 (i.e., in 2019), the percent of households with Internet subscription is approximately 91.47%.

Step5: Find x for 2024

For the year 2024, $x=2024 - 2010=14$
Substitute $x = 14$ into the equation $y = 2.13x+72.30$
$y=2.13\times14+72.30$

Step6: Calculate the product

$2.13\times14 = 30.82$
So, $y=30.82+72.30$

Step7: Calculate the sum

$y=30.82+72.30 = 103.12$

Step8: Analyze issues

One issue with the prediction for 2024 is that a percentage cannot exceed 100% in the context of the percent of households. The linear model may not be valid for long - term predictions as it does not account for saturation (when all households that can have an Internet subscription already do) or changes in technology, economic factors, or social trends that could affect Internet subscription rates.

Answer:

a. $(9,91.47)$
b. The ordered pair $(9,91.47)$ means that in 2019 (9 years after 2010), approximately 91.47% of households had an Internet subscription.
c. 103.12%
d. A percentage of households with Internet subscription cannot exceed 100%. The linear model may not hold for long - term predictions due to factors like market saturation and changes in technology, economic, and social trends.