https://file.aiquickdraw.com/mathbot/file/17280666184796dwbwtbe.jpg

Let's tackle the problems presented in the image one by one. I'll extract the relevant data and show you the calculations:

### Data Extracted:
| Year | Average Gas Price (Annual) ($) | Petroleum Import Price Index (June) |
|------|-------------------------------|-------------------------------------|
| 2012 | 3.680                         | 357.2                               |
| 2013 | 3.575                         | 364.9                               |
| 2014 | 3.437                         | 387.9                               |
| 2015 | 2.520                         | 226.1                               |
| 2016 | 2.250                         | 173.1                               |
| 2017 | 2.528                         | 178.7                               |
| 2018 | 2.813                         | 255.4                               |
| 2019 | 2.691                         | 236.6                               |
| 2020 | 2.258                         | 142.6                               |
| 2021 | 3.100                         | 267.6                               |
| 2022 | 4.059                         | 456.5                               |

### 1. Relative Changes (2019-2020)
#### Gas Price:
\[
\text{Relative Change} = \left( \frac{\text{2020 Price} - \text{2019 Price}}{\text{2019 Price}} \right) \times 100
\]
\[
\text{Relative Change} = \left( \frac{2.258 - 2.691}{2.691} \right) \times 100 \approx -16.10\%
\]

#### Petroleum Import Price Index:
\[
\text{Relative Change} = \left( \frac{142.6 - 236.6}{236.6} \right) \times 100 \approx -39.73\%
\]

### 2. Relative Changes (2020-2021)
#### Gas Price:
\[
\text{Relative Change} = \left( \frac{3.100 - 2.258}{2.258} \right) \times 100 \approx 37.28\%
\]

#### Petroleum Import Price Index:
\[
\text{Relative Change} = \left( \frac{267.6 - 142.6}{142.6} \right) \times 100 \approx 87.67\%
\]

### 3. Relative Changes (2012-2022)
#### Gas Price:
\[
\text{Relative Change} = \left( \frac{4.059 - 3.680}{3.680} \right) \times 100 \approx 10.29\%
\]

#### Petroleum Import Price Index:
\[
\text{Relative Change} = \left( \frac{456.5 - 357.2}{357.2} \right) \times 100 \approx 27.78\%
\]

### 4. Which Commodity is More Volatile?
Volatility refers to how much a price changes over time. Based on the relative percentage changes calculated:

- **Petroleum Import Price Index** shows much larger swings in percentage terms, such as an 87.67% increase from 2020 to 2021 and a 39.73% decrease from 2019 to 2020.
- **Gas Price** changes are significant but less drastic in comparison.

Thus, the **Petroleum Import Price Index** is more volatile.

---

Would you like a more detailed explanation of any of these steps or calculations? Here are some related questions for further exploration:

1. How do you calculate the percentage change between two values?
2. What factors might cause such a significant drop in the petroleum import price index between 2019 and 2020?
3. Can you explain how gas prices are connected to the petroleum import price index?
4. What external factors could contribute to volatility in oil and gas prices?
5. How might investors use volatility information to make financial decisions?

**Tip:** When calculating percentage changes, always ensure you're dividing by the correct base value (the initial year's value) to avoid miscalculations.

Using the data from the two consecutive years 2019-2020, 2020-2021, and 2012-2022, calculate the relative changes in gas price and petroleum import price. Round to the nearest hundredth of a percent.

This problem focuses on calculating the relative changes in gas and petroleum import prices between 2019-2020, 2020-2021, and 2012-2022 using percentage change formulas. It also explores the concept of volatility, a key factor for investors.

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