Question

the average price of tuition and fees at private 4-year colleges and universities increased from $8,800 in 1998 to $24,000 in 2014. calculate the relative change in price from 1998 to 2014 and compare it to the overall rate of inflation as measured by the consumer price index. average tuition and fees in private 4-year colleges and universities increased by \\(\square\\)% (round to the nearest integer as needed.) average annual cpi (1982-1984 = 100) \

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

Explanation:

Step1: Calculate the relative change formula

The formula for relative change is $\frac{\text{New Value}-\text{Old Value}}{\text{Old Value}}\times100\%$. Here, the old value (1998 tuition) is $a = 8800$ and the new value (2014 tuition) is $b=24000$.

Step2: Substitute values into the formula

Substitute $a = 8800$ and $b = 24000$ into $\frac{b - a}{a}\times100\%$. We get $\frac{24000-8800}{8800}\times100\%=\frac{15200}{8800}\times100\%$.

Step3: Simplify the fraction

$\frac{15200}{8800}=\frac{152}{88}=\frac{19}{11}\approx1.7273$. Then $1.7273\times 100\% = 172.73\%$.

Step4: Round the result

Rounding $172.73\%$ to the nearest integer gives $173\%$.

Answer:

$173$