To calculate the inflation rate from year 1 to year 2 using the Consumer Price Index (CPI), follow these steps:
1. Sum the CPI values for year 1:
Housing: 1200
Food: 360
Transportation: 180
Medical: 450
Education: 510
Apparel: 180
Recreation: 120
Other: 300
[tex]\[
\text{CPI for Year 1} = 1200 + 360 + 180 + 450 + 510 + 180 + 120 + 300 = 3300
\][/tex]
2. Sum the CPI values for year 2:
Housing: 1260
Food: 400
Transportation: 210
Medical: 550
Education: 620
Apparel: 190
Recreation: 90
Other: 310
[tex]\[
\text{CPI for Year 2} = 1260 + 400 + 210 + 550 + 620 + 190 + 90 + 310 = 3630
\][/tex]
3. Calculate the inflation rate:
The formula for calculating the inflation rate is given by:
[tex]\[
\text{Inflation Rate} = \left( \frac{\text{CPI for Year 2} - \text{CPI for Year 1}}{\text{CPI for Year 1}} \right) \times 100
\][/tex]
Substituting the values:
[tex]\[
\text{Inflation Rate} = \left( \frac{3630 - 3300}{3300} \right) \times 100
\][/tex]
Simplify the numerator first:
[tex]\[
3630 - 3300 = 330
\][/tex]
Then divide by the CPI for Year 1:
[tex]\[
\frac{330}{3300} = 0.1
\][/tex]
Finally, multiply by 100 to get the percentage:
[tex]\[
0.1 \times 100 = 10.0
\][/tex]
4. Round to the nearest tenth of a percent:
The inflation rate calculated is already at a tenth of a percent, which is 10.0%.
Therefore, the inflation rate from year 1 to year 2 is [tex]\( \boxed{10.0\%} \)[/tex].
