Question

watch the video and then solve the problem given below. click here to watch the video. people who are severely obese (bmi≥40) are at the most risk for serious health problems, which are the most expensive to treat. the percent of people in a country who are severely obese from 2000 and projected to 2030 are shown. complete parts a - b below. year 2000 2010 2015 2020 2025 2030 % severely obese 2.4 4.6 6.7 7.5 9.3 11.1 y = 0.289x+2.114 (use integers or decimals for any numbers in the equation. round to three decimal places as needed.) b. graph the model and the data set on the same axes, and comment on the fit. the window is 0,30,5 by 0,14,1. choose the correct answer below

Explanation:

Step1: Analyze the linear - model

The linear model is $y = 0.289x+2.114$, where $x$ represents the number of years since 2000.

Step2: Check the data - points and the line

We can take some data - points from the table. For 2000 ($x = 0$), $y=0.289\times0 + 2.114=2.114$ (close to 2.4 in the table). For 2010 ($x = 10$), $y=0.289\times10+2.114=2.89 + 2.114 = 5.004$ (close to 4.6 in the table). As we plot the points from the table and the line $y = 0.289x+2.114$ on the window $[0,30,5]$ by $[0,14,1]$, we note that the line should pass through or be close to the data - points.
The line has a positive slope of 0.289, indicating an increasing trend in the percentage of severely obese people over the years.
Looking at the graphs:

• In option A, the line seems to fit the data - points well. The data - points are close to the line, and the increasing trend is captured correctly.
• Option B has the line above the data - points in a way that does not match the general trend of the data.
• Option C has the line not passing through or close to the data - points as accurately as option A.
• Option D also has the line not fitting the data - points as well as option A.

Answer:

A.