Question

since 2014, desktop internet consumption has been on the decline in a certain region of the world. the average daily minutes y of desktop internet use per person in the region can be estimated by the equation y = - 1.6x + 47.2, where x represents the number of years since 2014. a. find the x - intercept of this equation. b. what does this x - intercept mean? c. use part (b) to comment on your opinion of the limitations of using equations to model real data. a. the x - intercept of the equation is (type an ordered pair. round each coordinate to the nearest tenth as needed.)

Explanation:

Step1: Recall x - intercept definition

Set \(y = 0\) in the equation \(y=-1.6x + 47.2\). So, \(0=-1.6x + 47.2\).

Step2: Solve for x

Add \(1.6x\) to both sides: \(1.6x=47.2\). Then \(x=\frac{47.2}{1.6}=29.5\). The ordered - pair for the x - intercept is \((29.5,0)\).

Step3: Interpret x - intercept meaning

The x - intercept means that approximately 29.5 years after 2014 (around 2043.5), the average daily minutes of desktop Internet use per person in the region will be 0 according to the model.

Step4: Comment on limitations

Equations used to model real - world data are often simplifications. There could be unforeseen technological changes, economic factors, or social trends that the equation does not account for. For example, new technologies might boost Internet use again or economic recessions could change usage patterns in ways not captured by the linear model.

Answer:

a. \((29.5,0)\)
b. It means that about 29.5 years after 2014, the average daily minutes of desktop Internet use per person in the region will be 0 according to the model.
c. Equations used to model real - world data are simplifications. There could be unforeseen technological, economic, or social factors not accounted for in the linear model.