Question

since 2012, 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 = - 1.7x + 46.8, where x represents the number of years since 2012. 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 concept

The x - intercept is found when y = 0. So we set y = 0 in the equation y=-1.7x + 46.8.
$$0=-1.7x + 46.8$$

Step2: Solve for x

First, add 1.7x to both sides of the equation:
$$1.7x=46.8$$
Then divide both sides by 1.7:
$$x=\frac{46.8}{1.7}\approx27.5$$
The x - intercept as an ordered pair is (27.5, 0).

Step3: Interpret x - intercept

The x - intercept represents the number of years since 2012 when the average daily minutes of desktop internet use per person in the region is 0.

Step4: Comment on limitations

The equation is a linear model. Real - world data may not follow a perfect linear trend. There could be external factors (new technologies, changes in social behavior) that the linear model does not account for. Also, the model is only valid within the range of data used to create it, and extrapolating too far beyond that range (e.g., many years after the data collection period) may lead to inaccurate predictions.

Answer:

a. (27.5, 0)
b. The x - intercept represents the number of years since 2012 when the average daily minutes of desktop internet use per person in the region is 0.
c. The linear model may not account for external factors like new technologies or changes in social behavior, and extrapolation beyond the data - collection range may lead to inaccuracies.