Answer :
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.
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.