Question

The Consumer Price Index (CPI) is a measure of the change in the cost of goods over time. If 1982 is used as the base year of comparison in some country (CPI = 100 in 1982), then the CPI of 212.8 in 2006 would indicate that an item that cost $1.00 in 1982 would cost $2.13 in 2006 in this country. It is known that the CPI in this country has been increasing at an approximately linear rate for the past 30 years. A) Use this information to determine a linear function for this data, letting x be the years since 1982. B) Based on your function, what was the CPI in 2000? Compare the estimate to the actual CPI of 186 for this country. C) How is the annual CPI changing? A) y = ( ) x + ( ) Round to the nearest tenth as needed. 

          The Consumer Price Index (CPI) is a measure of the change in the cost of goods over time. If 1982 is used as the base year of comparison in some country (CPI = 100 in 1982), then the CPI of 212.8 in 2006 would indicate that an item that cost $1.00 in 1982 would cost $2.13 in 2006 in this country. It is known that the CPI in this country has been increasing at an approximately linear rate for the past 30 years.

A) Use this information to determine a linear function for this data, letting x be the years since 1982.

B) Based on your function, what was the CPI in 2000? Compare the estimate to the actual CPI of 186 for this country.

C) How is the annual CPI changing?

A) y = (   ) x + (   )
Round to the nearest tenth as needed.
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Elementary and Intermediate Algebra
Elementary and Intermediate Algebra
Alan S. Tussy, R. David Gustafson 5th Edition
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The Consumer Price Index (CPI) is a measure of the change in the cost of goods over time. If 1982 is used as the base year of comparison in some country (CPI = 100 in 1982), then the CPI of 212.8 in 2006 would indicate that an item that cost $1.00 in 1982 would cost $2.13 in 2006 in this country. It is known that the CPI in this country has been increasing at an approximately linear rate for the past 30 years. A) Use this information to determine a linear function for this data, letting x be the years since 1982. B) Based on your function, what was the CPI in 2000? Compare the estimate to the actual CPI of 186 for this country. C) How is the annual CPI changing? A) y = ( ) x + ( ) Round to the nearest tenth as needed.
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Transcript

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00:01 The consumer price index, cpi, is a measure of the change in the cost of goods over time.
00:05 If 1982 is used as the base year of comparison in some country, where the cpi in 1982 is 100, then the cpi of 220 in 2006 would indicate that an item cost, that an item that cost a dollar in 1982 would now cost $2 .13 in 2006.
00:24 It is known that the cpi for this country has been increasing in an approximate linear rate for the past 30.
00:30 30 years.
00:31 All right, so here we have linear that's going to tell us that we should use a slope intercept form model here.
00:38 So let's find the slope.
00:40 We know that we start or we end up at 212 .8 going up from 100, and it took us from 1982 to 2006.
00:54 Well, 2006 minus 1882 will tell us that that is 24 years.
01:01 So it went from 100 to 212 in 24 years.
01:05 So 212 .8 minus 100 divided by 24 is going to give us a slope of 4 .7.
01:14 So we're going to put our slope in here, 4 .7x.
01:18 And then we need to think about our y intercept.
01:21 Remember in a word problem, the y intercept is going to be your initial value.
01:25 What did the index start at? well, in this case, the index.
01:29 Started at 100.
01:31 So our linear model is going to be y equals 4 .7x plus 100...
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