Question

what does the index value of 182.1 in 2010 mean? explain your reasoning
choose the correct answer below
a. gas in 2010 cost 182.1¢ per gallon, because the gas price index measures the cost per gallon
b. gas in 2010 cost 1821¢ per gallon, because the gas price index measures the cost per gallon
c. gas in 2010 cost 1.821 times as much as gas in 2000, because the ratio of the gas price index in 2010 to the gas price index in 2000 is 1.821
d. gas in 2010 cost 182.1 times as much as gas in 2000, because because the ratio of the gas price index in 2010 to the gas price index in 2000 is 182.1

Explanation:

A price index compares the price of a good in a given year to its price in a base year. Here, the base year is 2000 (index = 100). The formula for the price - index is \(I=\frac{P_{t}}{P_{0}}\times100\), where \(P_{t}\) is the price in year \(t\) and \(P_{0}\) is the price in the base year.

If \(I_{2010} = 182.1\) and \(I_{2000}=100\), then \(\frac{I_{2010}}{I_{2000}}=\frac{P_{2010}}{P_{2000}}\).

Answer:

D. Gas in 2010 cost 182.1 times as much as gas in 2000, because the ratio of the gas price index in 2010 to the gas price index in 2000 is 182.1.