To determine the Consumer Price Index (CPI) for 2014 and the inflation rate, we can follow these steps:
1. Calculate the cost of the basket for the base year (2012):
- The price of an apple in 2012 is \[tex]$2, and the number of apples consumed is 3.
\[
\text{Cost of apples in 2012} = 2 \, (\text{price per apple}) \times 3 \, (\text{number of apples}) = 6
\]
- The price of an orange in 2012 is \$[/tex]3, and the number of oranges consumed is 2.
[tex]\[
\text{Cost of oranges in 2012} = 3 \, (\text{price per orange}) \times 2 \, (\text{number of oranges}) = 6
\][/tex]
- Total cost of the basket in 2012:
[tex]\[
\text{Total cost in 2012} = 6 \, (\text{cost of apples}) + 6 \, (\text{cost of oranges}) = 12
\][/tex]
2. Calculate the cost of the basket for the year 2014:
- The price of an apple in 2014 is \[tex]$5, and the number of apples consumed is 1.
\[
\text{Cost of apples in 2014} = 5 \, (\text{price per apple}) \times 1 \, (\text{number of apples}) = 5
\]
- The price of an orange in 2014 is \$[/tex]5, and the number of oranges consumed is 2.
[tex]\[
\text{Cost of oranges in 2014} = 5 \, (\text{price per orange}) \times 2 \, (\text{number of oranges}) = 10
\][/tex]
- Total cost of the basket in 2014:
[tex]\[
\text{Total cost in 2014} = 5 \, (\text{cost of apples}) + 10 \, (\text{cost of oranges}) = 15
\][/tex]
3. Calculate the Consumer Price Index (CPI) for 2014:
- The CPI is calculated as:
[tex]\[
\text{CPI}_{2014} = \left( \frac{\text{Total cost in 2014}}{\text{Total cost in 2012}} \right) \times 100
\][/tex]
- Substituting the values:
[tex]\[
\text{CPI}_{2014} = \left( \frac{15}{12} \right) \times 100 = 1.25 \times 100 = 125
\][/tex]
4. Calculate the inflation rate from 2012 to 2014:
- The inflation rate is given by:
[tex]\[
\text{Inflation rate}_{2014} = \left( \frac{\text{CPI}_{2014} - 100}{100} \right) \times 100
\][/tex]
- Substituting the CPI value:
[tex]\[
\text{Inflation rate}_{2014} = \left( \frac{125 - 100}{100} \right) \times 100 = 0.25 \times 100 = 25\%
\][/tex]
Based on the calculations, the CPI for 2014 is 125, and the inflation rate from 2012 to 2014 is 25%. The correct answer is:
E. [tex]\( 125 \, \text{CPI}, 50.60 \, \text{percent inflation} \)[/tex]
However, based on the steps outlined above, this does not match any of the provided choices exactly. The Python solution indicates that there might be an error in the prompted answer set.
