Question

the average price of a low - fare airline ticket rose from $270 in 1997 to $410 in 2017. calculate the relative change in price from 1997 to 2017, and compare it to the overall rate of inflation as measured by the consumer price index.
low - fare airline ticket prices increased by \\(\square\\)%.
(round to the nearest integer as needed.)
average annual cpi (1982 - 1984 = 100)
\

$$\begin{tabular}{ccc|ccc|ccc} \\hline year & cpi & & year & cpi & & year & cpi \\\\ 1982 & 96.5 & & 1995 & 152.4 & & 2008 & 215.3 \\\\ 1983 & 99.6 & & 1996 & 156.9 & & 2009 & 214.5 \\\\ 1984 & 103.9 & & 1997 & 160.5 & & 2010 & 218.1 \\\\ 1985 & 107.6 & & 1998 & 163.0 & & 2011 & 224.9 \\\\ 1986 & 109.6 & & 1999 & 166.6 & & 2012 & 229.6 \\\\ 1987 & 113.6 & & 2000 & 172.2 & & 2013 & 233.0 \\\\ 1988 & 118.3 & & 2001 & 177.1 & & 2014 & 236.7 \\\\ 1989 & 124.0 & & 2002 & 179.9 & & 2015 & 237.0 \\\\ 1990 & 130.7 & & 2003 & 184.0 & & 2016 & 240.0 \\\\ 1991 & 136.2 & & 2004 & 188.9 & & 2017 & 245.1 \\\\ 1992 & 140.3 & & 2005 & 195.3 & & 2018 & 251.1 \\\\ 1993 & 144.5 & & 2006 & 201.6 & & 2019 & 255.7 \\\\ 1994 & 148.2 & & 2007 & 207.3 & & 2020 & 258.8 \\\\ & & & & & & 2021 & 271.0 \\\\ \\hline \\end{tabular}$$

Explanation:

Step1: Calculate the absolute change

The absolute change formula is \( \text{Absolute Change}= \text{New Value}-\text{Old Value}\).
Here, the old value (price in 1997) is \(a = 270\) and the new value (price in 2017) is \(b=410\).
So, \(\text{Absolute Change}=410 - 270=140\).

Step2: Calculate the relative change

The relative change formula is \( \text{Relative Change}=\frac{\text{Absolute Change}}{\text{Old Value}}\times100\%\).
Substitute the values: \(\text{Relative Change}=\frac{140}{270}\times 100\%\).
\(\text{Relative Change}=\frac{14000}{270}\% \approx 51.85\%\).
Rounding to the nearest integer, we get \(52\%\).

Answer:

\(52\)