To determine the percentage increase in inflation between 2010 and 2015 using the provided Consumer Price Index (CPI) data, follow these steps:
1. Identify the CPI values for the relevant years:
- CPI in January 2010: 216.687
- CPI in January 2015: 233.707
2. Calculate the change in CPI:
Subtract the CPI of 2010 from the CPI of 2015.
[tex]\[
\Delta \text{CPI} = \text{CPI}_{2015} - \text{CPI}_{2010}
\][/tex]
[tex]\[
\Delta \text{CPI} = 233.707 - 216.687 = 17.02
\][/tex]
3. Calculate the percentage increase in CPI:
To find the percentage increase, divide the change in CPI by the CPI of 2010 and multiply by 100.
[tex]\[
\text{Percentage Increase} = \left( \frac{\Delta \text{CPI}}{\text{CPI}_{2010}} \right) \times 100
\][/tex]
Substituting the values:
[tex]\[
\text{Percentage Increase} = \left( \frac{17.02}{216.687} \right) \times 100 \approx 7.85
\][/tex]
Therefore, the inflation increased by approximately 7.85 percent between 2010 and 2015.
The correct answer is C. 7.85 percent.
