An economy's consumer price index (CPI) is described by the function , where corresponds to 1995. At what rate was the CPI changing in 2002?
A)12.3 pts/yr
B)12.6 pts/yr
C)12.5 pts/yr
D)12.4 pts/yr
E)12.7 pts/yr

Question

An economy's consumer price index (CPI) is described by the function  , where  corresponds to 1995. At what rate was the CPI changing in 2002?
A)12.3 pts/yr 
B)12.6 pts/yr 
C)12.5 pts/yr 
D)12.4 pts/yr 
E)12.7 pts/yr

Quizplus · Accepted Answer

To find the rate of change of the CPI in 2002, we need to take the derivative of the CPI with respect to time (t) and evaluate at t=7 (since the CPI function is given in terms of the year, with t=0 corresponding to 1995, t=7 corresponds to 2002).

So, taking the derivative of the given function:
CPI'(t) = 11eb12b0_aa36_9555_b394_168ca5fd5d5d_TB7866_11

Evaluating at t=7:
CPI'(7) = 11e7(bln(1.0396)) = 12.6

So the rate of change of the CPI in 2002 was 12.6 pts/yr. Therefore, the best choice is B.

An Economy's Consumer Price Index (CPI) Is Described by the Function