Question

suppose you needed $0.26 to buy a particular box of macaroni and cheese in 1983. how much would it cost to buy the same box of macaroni and cheese in 2010? assume that all prices have risen at the same rate as the cpi. how much would it cost? $\square$ (round to the nearest cent.) average annual cpi (1982-1984 = 100) \

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

Explanation:

Step1: Identify the CPI values

From the table, \(CPI_{1983} = 99.6\) and \(CPI_{2010}=218.1\)

Step2: Use the CPI formula for price adjustment

The formula to adjust a price \(P\) from an earlier year \(y_1\) to a later year \(y_2\) is \(P_{y_2}=P_{y_1}\times\frac{CPI_{y_2}}{CPI_{y_1}}\)
Here, \(P_{1983} = 0.26\), so \(P_{2010}=0.26\times\frac{218.1}{99.6}\)

$$
LATEXBLOCK0
$$

Step3: Round to the nearest cent

Rounding \(0.569337\) to the nearest cent (two decimal places), we look at the third - decimal place. Since \(9\gt5\), we round up. So \(0.569337\approx0.57\)

Answer:

\(0.57\)