Problem

The Consumer Price Index (CPI) is a measure of inflation obtained by comparing current prices with base prices in 1982-84. Use this information to complete the missing item in the following table for ice cream. \begin{tabular}{|c|c|c|c|} \hline Item & $\begin{array}{c}\text { CPI for Item in } \\ 2000\end{array}$ & $\begin{array}{c}\text { CPI for Item in } \\ 2009\end{array}$ & $\begin{array}{c}\text { Percent of } \\ \text { Increase }\end{array}$ \\ \hline Ice cream & 160.1 & 202.8 & \\ \hline \end{tabular} The percent of increase is \%. (Round to one decimal place as needed.)

Solution

Step 1 :Given the Consumer Price Index (CPI) for ice cream in 2000 is 160.1 and in 2009 is 202.8.

Step 2 :The percent of increase can be calculated by subtracting the initial value from the final value, dividing the result by the initial value, and then multiplying by 100 to get a percentage.

Step 3 :Let's denote the initial value as \(I\) and the final value as \(F\). In this case, \(I = 160.1\) and \(F = 202.8\).

Step 4 :The formula for percent increase is \(\frac{F - I}{I} \times 100\%\).

Step 5 :Substitute \(I\) and \(F\) into the formula, we get \(\frac{202.8 - 160.1}{160.1} \times 100\%\).

Step 6 :The percent of increase is approximately 26.670830730793266.

Step 7 :Round to one decimal place as needed, the percent of increase is 26.7.

Step 8 :Final Answer: The percent of increase is \(\boxed{26.7\%}\).

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