Question

the average price of tuition and fees at public 4-year colleges and universities increased from $1,750 in 1998 to $6,900 in 2013. calculate the relative change in price from 1998 to 2013 and compare it to the overall rate of inflation as measured by the consumer price index. average tuition and fees in public 4-year colleges and universities increased by \\(\square\\)%. (round to the nearest integer as needed.) average annual cpi (1982-1984 = 100) \

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

Explanation:

Step1: Calculate the absolute change

The formula for absolute change is \( \text{Absolute Change}=\text{New Value}-\text{Old Value}\).
Here, the old value (in 1998) \(a = 1750\) and the new value (in 2013) \(b=6900\).
So, \( \text{Absolute Change}=6900 - 1750=5150\).

Step2: Calculate the relative change

The formula for relative change is \( \text{Relative Change}=\frac{\text{Absolute Change}}{\text{Old Value}}\times100\%\).
Substitute the values: \( \text{Relative Change}=\frac{5150}{1750}\times 100\%\).
\(\frac{5150}{1750}\times100\%=\frac{515000}{1750}\% \approx 294.29\%\)

Answer:

\(294\)