Problems 69–72 require the following discussion. The consumer price index (CPI) indicates the relative change in price over time for a fixed basket of goods and services. It is a cost-of-living index that helps measure the effect of inflation on the cost of goods and services. The CPI uses the base period 1982–1984 for comparison (the CPI for this period is 100). The CPI for February 2022 was 283.72. This means that $100 in the period 1982–1984 had the same purchasing power as $283.72 in February 2022. In general, if the rate of inflation averages r% per annum over n years, then the CPI after n years is

where CPI₀ is the CPI at the beginning of the n-year period.

If the average annual inflation rate is 3.1%, how long will it take for the CPI to double? (A doubling of the CPI means purchasing power is cut in half.)

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CPI = CPI (1 + 100