Question

the average price of tuition and fees at private 4-year colleges and universities increased from $8,400 in 1997 to $22,000 in 2015. calculate the relative change in price from 1997 to 2015 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 % (round to the nearest integer as needed.) average annual cpi (1982 - 1984 = 100) year cpi year cpi year cpi 1982 90.5 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 224.0 1986 109.6 1999 166.6 2012 229.6 1987 113.6 2000 172.2 2013 235.0 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

Explanation:

Step1: Recall relative change formula

The formula for relative change is $\frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \times 100\%$.
Here, the old value (1997) is $8400$, and the new value (2015) is $22000$.

Step2: Calculate the difference

First, find the difference between the new and old values: $22000 - 8400 = 13600$.

Step3: Compute relative change

Now, apply the formula: $\frac{13600}{8400} \times 100\%$.
Calculate $\frac{13600}{8400} \approx 1.6190$, then multiply by $100\%$: $1.6190 \times 100\% = 161.90\%$.

Step4: Round to nearest integer

Rounding $161.90\%$ to the nearest integer gives $162\%$.

Answer:

162