Final answer:
The linear equation modeling CPI is y = 3.62x + 183.38. The estimated CPI in 2012 is 226.82 and in 2013 is 230.44. The correct answer is option C .
Step-by-step explanation:
The question asks us to find the linear equation that models the Consumer Price Index (CPI) between the years 2011 and 2016, and to use that equation to estimate the CPI in the years 2012 and 2013. Given that the CPI in 2011 was 223.2 (x = 11), and in 2016 it was 241.3, we can calculate the slope of the linear equation by using the formula for slope (m) which is (change in y)/(change in x), resulting in (241.3 - 223.2) / (16 - 11) = 18.1 / 5 = 3.62.
To find the linear equation modeling CPI, we can use the given information for 2011 and 2016. Let's assign x = 11 to correspond to the year 2011 and x = 16 to correspond to the year 2016. We have two points (11, 223.2) and (16, 241.3).
Using the formula for the equation of a line, y = mx + b, we can substitute the values of the points to find the slope (m) and y-intercept (b).
slope (m) = (241.3 - 223.2) / (16 - 11) = 18.1 / 5 = 3.62
y-intercept (b) = 223.2 - (3.62 * 11) = 223.2 - 39.82 = 183.38
The linear equation modeling CPI is y = 3.62x + 183.38.
To estimate CPI in 2012, let's substitute x = 12 into the equation. CPI in 2012 = 3.62 * 12 + 183.38 = 43.44 + 183.38 = 226.82.
To estimate CPI in 2013, let's substitute x = 13 into the equation. CPI in 2013 = 3.62 * 13 + 183.38 = 47.06 + 183.38 = 230.44.
Therefore, the correct answer is c) CPI in 2012: 226.82 and CPI in 2013: 230.44.