If it cost \[tex]$9 to fill a gas tank in 1980, how much would it cost in 1990?

\[

\begin{tabular}{|l|c|c|c|}

\hline

Year & Price & \begin{tabular}{c}

Price as a Percentage \\

of 1980 Price

\end{tabular} & \begin{tabular}{c}

Price Index \\

(1980=100)

\end{tabular} \\

\hline

1960 & \$[/tex]0.31 & 25.4\% & 25.4 \\
1970 & \[tex]$0.36 & 29.5\% & 29.5 \\

1980 & \$[/tex]1.22 & 100.0\% & 100.0 \\
1990 & \[tex]$1.23 & 100.8\% & 100.8 \\

2000 & \$[/tex]1.56 & 127.9\% & 127.9 \\
2010 & \[tex]$2.84 & 232.8\% & 232.8 \\

\hline

\end{tabular}

\]

It would have cost \$[/tex] [tex]$\square$[/tex] in 1990. (Round to the nearest cent as needed.)

To determine how much it would have cost in 1990 to fill a gas tank that cost [tex]$9 in 1980, we can use the concept of a price index. A price index measures the relative change in prices over time, and in this case, it is expressed with 1980 as the base year (1980 = 100).

Here's a step-by-step solution:

1. Understand the Price Index:
- In 1980, the price index is 100, so the cost of $[/tex]9 corresponds to this index.
- By 1990, the price index increased to 100.8.

2. Calculate the Price in 1990:
- We know that the 1980 cost is [tex]$9, and we need to adjust for the price index in 1990.
- The price index in 1990 is 100.8, so we use it to find the equivalent cost in 1990.

3. Cost Calculation:
- The cost in 1990 can be calculated using the formula:
\[
\text{Cost in 1990} = \left( \frac{\text{Price Index in 1990}}{\text{Price Index in 1980}} \right) \times \text{Cost in 1980}
\]
- Substitute the known values:
\[
\text{Cost in 1990} = \left( \frac{100.8}{100} \right) \times 9
\]
- Calculate the result:
\[
\text{Cost in 1990} = 1.008 \times 9 = 9.072
\]

4. Round the Result:
- Rounding $[/tex]9.072 to the nearest cent gives [tex]$9.07.

Therefore, in 1990, it would have cost approximately $[/tex]9.07 to fill the gas tank.