SOLUTION: 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 fo
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Question 978523: 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 2008, reflecting buying patterns of all urban consumers, with x representing years past 1900.
Year
Consumer
Price Index Year
Consumer
Price Index
1940 14 1990 130.7
1950 24.1 2000 172.2
1960 29.6 2005 195.3
1970 38.8 2008 215.3
1980 82.4
(a) Find an equation that models these data. (Round your coefficients to three decimal places.)
y =
Incorrect: Your answer is incorrect.
(b) Use the model to predict the consumer price index in 2017. (Round your answer to one decimal place.)
(c) According to the model, during what year will the consumer price index pass 300?
You can put this solution on YOUR website! Let
x = number of years since 1900 (x = 0 represents 1900, x = 1 represents 1901, etc)
y = CPI for a given year x years after 1900
CPI = Consumer Price Index
Year
CPI
40
14
50
24.1
60
29.6
70
38.8
80
82.4
90
130.7
100
172.2
105
195.3
108
215.3
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a)
Use a calculator (like a TI83) or excel to find the equation of the regression line.
If you have neither, then use this free online calculator and it will get the job done.
The regression line is (this is approximate)
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b)
Plug in x = 117 (Note: 2017 - 1900 = 117) to find the predicted CPI in 2017
I rounded the result to 1 decimal place because all of the other CPI values are shown accurate to 1 decimal place.
The predicted CPI in the year 2017 is 220.7
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c)
Plug in and solve for x
Round to the nearest whole number to get
It will take 143 years for the CPI to pass 300. So the CPI will pass 300 in the year 1900+143 = 2043
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