Question

The 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 ​(CPIequals100 in​ 1982), then the CPI of 200.8 in 2006 would indicate that an item that cost $ 1.00 in 1982 would cost $ 2.01 in 2006 in this country. It is known that the CPI in this country has been increasing at an approximately linear rate for the past 30 years.

a. Use this information to determine a linear function for this​ data, letting x be the years since 1982.

b. Based on your​ function, what was the CPI in​ 2000? Compare this estimate to the actual CPI of 177.3 for this country.

c. How is the annual CPI​ changing?

y=(_)x+(_) (Round to the nearest tenth as needed)

Answer 1

ANSWER:

The 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 ​(CPIequals100 in​ 1982), then the CPI of 200.8 in 2006 would indicate that an item that cost $ 1.00 in 1982 would cost $ 2.01 in 2006 in this country. It is known that the CPI in this country has been increasing at an approximately linear rate for the past 30 years.

cpi=y

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

x at 2006= 2006-1982=24===>point(x2,y2)=(24,200.8)

slope of linear function =(200.8-100)/(24-0) =4.2

let the linear equation be

y=mx+c

100=m*0+c

==>c=100

so equation is y=4.2x +100

b)cpi in 2000

x in 2000 =2000-1982=18

cpi=4.2*18+100

cpi=175.6

c)cpi is changing at 4.2 units per year