UpStudy Free Solution:

To determine which scenario reflects an annual inflation rate of \(3\% \), we can calculate the price increase for each item and compare it to the expected increase of \(3\% \).

For the computer:

Year 1 price: \(325.00\)

Year 2 price: \(328.00\)

Expected Year 2 price with \(3\% \) inflation: 
\[325 \times 1.03 = 334.75\]

The actual increase is:
\[328 - 325 = 3 \quad ( \text { which is less than } 3\% ) \]

For the soda:

Year 1 price: \(0.75\)

Year 2 price: \(0.78\)

Expected Year 2 price with \(3\% \) inflation: 
\[0.75 \times 1.03 = 0.7725 \approx 0.77\]

The actual increase is:
\[0.78 - 0.75 = 0.03 \quad ( \text { which is 4\% } ) \]

For the board game:

Year 1 price: \(10.00\)

Year 2 price: \(10.03\)

Expected Year 2 price with \(3\% \) inflation: 
\[10 \times 1.03 = 10.30\]

The actual increase is:
\[10.03 - 10.00 = 0.03 \quad ( \text { which is 0.3\% } ) \]

For the sofa:

Year 1 price: \(500.00\)

Year 2 price: \(515.00\)

Expected Year 2 price with \(3\% \) inflation: 
\[500 \times 1.03 = 515\]

The actual increase is:
\[515 - 500 = 15 \quad ( \text { which is 3\% } ) \]
The correct answer is:
D. In year 1, the price of a sofa is \(500.00\). In year 2, the same sofa costs \(515.00\).
 

Supplemental Knowledge

Inflation is the rate at which the general level of prices for goods and services rises, eroding purchasing power. The annual inflation rate is calculated as the percentage increase in prices over a year.
To determine if a price change reflects an annual inflation rate of \(3\% \), we use the formula:
\[\text { New Price} = \text { Old Price} \times ( 1 + \text { Inflation Rate} ) \]
For an inflation rate of \(3\% \):
\[\text { New Price} = \text { Old Price} \times 1.03\]
Let's apply this formula to each scenario to see which one matches a \(3\% \) increase.

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