Final answer:
To find a linear equation relating the percentage of smokers to the years since 2015, use the point-slope form of a linear equation with the given data points. The linear equation is y = -1.33x + 2676.35. To predict the year in which the percentage of smokers will fall below 5%, solve the linear equation for when y = 0.05, which gives the year as 2011.
Step-by-step explanation:
To find a linear equation relating the percentage of smokers (s) to the years since 2015 (t), we need to use the two data points given: (2015, 29.9%) and (2022, 17.9%).
We can use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. In this case, the two points are (2015, 29.9%) and (2022, 17.9%).
The slope (m) can be found using the formula (change in y) / (change in x), which is (17.9 - 29.9) / (2022 - 2015). Simplifying this, we get m = -1.33.
Now we can substitute the values of one of the points and the slope into the point-slope form to get the linear equation. Let's use (2015, 29.9%).
Using (x1, y1) = (2015, 29.9%) and m = -1.33, the equation becomes y - 0.299 = -1.33(x - 2015).
Simplifying this equation gives the linear equation relating the percentage of smokers to the years since 2015 as y = -1.33x + 2676.35.
To predict the year in which the percentage of smokers will fall below 5%, we need to solve the linear equation for when y = 0.05 (5%).
Substituting y = 0.05 into the equation -1.33x + 2676.35 gives 0.05 = -1.33x + 2676.35.
Solving for x, we get x = (0.05 - 2676.35) / -1.33 = -2010.8. Since years cannot be negative, we round up to the nearest whole number, which is 2011.
Therefore, the year in which the percentage of smokers will fall below 5% is 2011.