SOLUTION: Use the inflation proportion to estimate the 2005 price of a jacket which costs $470 in 2002. Assume that the price increased at the average annual rate shown in the table below. R

Question 1042208: Use the inflation proportion to estimate the 2005 price of a jacket which costs $470 in 2002. Assume that the price increased at the average annual rate shown in the table below. Round your answer to the nearest dollar.
Year Average CPI-U Percent Change in CPI-U
1999 166.6 2.2
2000 172.2 3.4
2001 177.1 2.8
2002 179.9 1.6
2003 184.0 2.3
2004 188.9 2.7
2005 195.3 3.4

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the table shows the consumer price index in the year indicated and the percent growth rate in that index from the previous year.

for example:

1999 166.6 2.2
2000 172.2 3.4
2001 177.1 2.8 *****
2002 179.9 1.6 *****
2003 184.0 2.3 *****
2004 188.9 2.7
2005 195.3 3.4

in 2002 the consumer price index was 179.9.
in 2003, the consumer price index was 184.0.
this represented a 2.3% increase from what it was in 2002.
in 2004, the consumer price index was 188.9.
this represented a 2.7% increase from what it was in 2003.
in 2005, the consumer price index was 195.3.
this represented a 3.4% increase from 2004.

you bought the jacket in 2002 and it cost you 470.

in 2003, the price would have increased 2.3%.
in 2004, the price would have increased an additional 2.7%.
in 2005, the price would have increased an additional 3.4%.

an increase of 2.3% is the same as multiplying by a factor of 1.023.
an increase of 2.7% is the same as multiplying by a factor of 1.027.
an increase of 3.4% is the same as multiplying by a factor of 1.034.

the price was 470 in 2002.
the price would be 470 * 1.023 in 2003.
the price would be 470 * 1.023 * 1.027 in 2004.
the price would be 470 * 1.023 * 1.027 * 1.034 in 2005.

470 * 1.023 * 1.027 * 1.034 = 510.5807936.

round that to the nearest dollars and you get 511.

the price would have been 511 in 2005, based on the percent increases indicated in the table.

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