A consumer price index (CPI) is a measure of the change in the cost of goods ove

Question

A consumer price index (CPI) is a measure of the change in the cost of goods over time. If 1982 is used as the base year of comparison in some country (CPI = 100 in 1982), then the CPI of 215.2 in in 2006 would indicate that the cost in $1 in 1982 is $2.15 in 2006 in this country. It is known that the CPI in the country has been increasing at an approx. linear rate for the past 30 years. Use this information to determine a linear function for this data, letting x be the years since 1982. Based on your function what was the CPI in 2001? How is the annual CPI changing?

Explanation / Answer

cpi=y

x at 1982=0   ==> point (x1,y1)=(0,100)

x at 2006= 2006-1982=24===>point(x2,y2)=(24,215.2)

slope of linear function =(215.2-100)/(24-0) =4.8

let the linear equation be

y=mx+c

100=m*0+c

==>c=100

so equation is y=4.8x +100

b)cpi in 2001

x in 2001 =2001-1982=19

cpi=4.8*19 +100

cpi=191.2

c)cpi is changing at 4.8 units per year

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