Exercise $2($Consumer Price Index $($CPI$)).$ 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 January $2006$ was $198\mathrm{.}3.$ This means that $$100$ in the period $1982-1984$ had the same purchasing power as $$198\mathrm{.}30$ in January $2006.$ In general, if the rate of inflation averages $r$ per annum over $n$ years, then the CPI index after $n$ years is CPI $=$CPI$0((1+\frac{r}{100}{)}^n$

where is the CPI $(0$ index at the beginning of the $n-$year period.

Source: U$.$S$.$ Bureau of Labor Statistics

$($a$)$ The CPI was $163\mathrm{.}0$ for $1998$ and $215\mathrm{.}3$ for $2008.$ Assuming that annual inflation remained constant for this time period, determine the average annual inflation rate.

$($b$)$ Using the inflation rate from part $($a$),$ in what year will the CPI reach $300?$

$2$