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------------------------------------------------ Daily Problem #4

Your contributions should demonstrate critical thinking about the topic. Use methods shown in class only.

Submission Options:

1. Online Submission:
- Click "Daily Problem #4" in your post to upload your solutions.
- Click "Add submission" at the bottom of the post.
- Upload your file as a PDF.
- Click "Save changes" to submit your answer.
- Note: Online submissions close at 12:00 p.m. on Thursday, January 30, 2025, in HFC Online.

2. In-Class Submission:
- Submit your answer sheet to the instructor in class.
- Deadline is before 12:00 p.m. on Thursday, January 30, 2025.

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Problem:

If it cost \[tex]$12 to fill a gas tank in 1985, how much would it have cost to fill the same tank in 2015? Show the original substitution of numbers into the formula with labels. Then simplify your answer with labels and units. Round your final answer to two decimal places.

Table 3.2: Average Gasoline Prices (per gallon)

\[
\begin{array}{|c|c|c|c|}
\hline
\text{Year} & \text{Price} & \text{Price as a Percentage of 1985 Price} & \text{Price Index (1985=100)} \\
\hline
1965 & \$0.31 & 25.8\% & 25.8 \\
\hline
1975 & \$0.57 & 47.5\% & 47.5 \\
\hline
1985 & \$1.20 & 100.0\% & 100.0 \\
\hline
1995 & \$1.21 & 100.8\% & 100.8 \\
\hline
2005 & \$2.31 & 192.5\% & 192.5 \\
\hline
2015 & \$2.52 & 210.0\% & 210.0 \\
\hline
\end{array}
\]

Source: U.S. Department of Energy; prices are the year-long average for all grades of gasoline.

To find out how much it would have cost to fill the same gas tank in 2015, we need to use the price index values from the given table.

Here's the step-by-step process:

1. Understand the Values:
- In 1985, the cost to fill the gas tank was [tex]$12.
- The price index for 1985 is given as 100.0.
- The price index for 2015 is 210.0.

2. Use the Price Index to Calculate the Cost in 2015:
The price index indicates how much prices have changed compared to the base year, which is 1985 in this case.

3. Formula for Cost in 2015:
We can use the formula to find the adjusted cost:

\[
\text{Cost in 2015} = \text{Cost in 1985} \times \left(\frac{\text{Price Index in 2015}}{\text{Price Index in 1985}}\right)
\]

4. Substitute the Values into the Formula:
\[
\text{Cost in 2015} = 12.0 \times \left(\frac{210.0}{100.0}\right)
\]

5. Simplify the Calculation:
- First divide 210.0 by 100.0, which equals 2.1.
- Then multiply 12.0 by 2.1 to get 25.2.

6. Rounded Final Answer:
Since we need to round to two decimal places, the final cost to fill the gas tank in 2015 is $[/tex]25.20.

This step-by-step approach shows that in 2015, it would have cost $25.20 to fill the same gas tank as it did in 1985.