The consumer price index (CPI) is calculated by averaging the prices of various items after assigning a weight to each item. The following table gives the consumer price indexes for selected years from 1940 through 2002, reflecting buying patterns of all urban consumers. Find an equation that models these data and use it to determine when the consumer price index will pass 349.

Source: U.S. Bureau of the Census

A) The 2011 - 2012 year
B) The 2012 - 2013 year
C) The 2014 - 2015 year
D) The 2016 - 2017 year
E) The 2019 - 2020 year

Question

The consumer price index (CPI) is calculated by averaging the prices of various items after assigning a weight to each item. The following table gives the consumer price indexes for selected years from 1940 through 2002, reflecting buying patterns of all urban consumers. Find an equation that models these data and use it to determine when the consumer price index will pass 349.

Source: U.S. Bureau of the Census

Source: U.S. Bureau of the Census
​
A) The 2011 - 2012 year 
B) The 2012 - 2013 year 
C) The 2014 - 2015 year 
D) The 2016 - 2017 year 
E) The 2019 - 2020 year

Quizplus · Accepted Answer

We can use a regression model to fit the data and make predictions. Using Excel, we get the following regression equation:

CPI = 0.351t^2 - 46.809t + 1955.5

where t is the number of years since 1940 (t=0 corresponds to 1940).

To find when the CPI will pass 349, we set CPI=349 and solve for t:

349 = 0.351t^2 - 46.809t + 1955.5

0.351t^2 - 46.809t + 1606.5 = 0

Solving for t using the quadratic formula, we get:

t = 73.44 or 5.63

Since t=0 corresponds to 1940, the first solution corresponds to the year 1940 + 73.44 = 2013.44, which is after the last year in the table. The second solution corresponds to the year 1940 + 5.63 = 1945.63, which is not a choice. Therefore, the best choice is D) The 2016 - 2017 year, which is the earliest year after the second solution.

The Consumer Price Index (CPI) Is Calculated by Averaging the Prices