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The Rivera and Patel families each bought a car at the same time. The resale values, in dollars, of each car are modeled by these functions, where [tex]$x$[/tex] is the number of years that the family has owned the car.

[tex]\[
\begin{tabular}{|c|c|}
\hline
Rivera Family Car & Patel Family Car \\
\hline
$f(x)=21,249(0.88)^x$ & $g(x)$ \\
\hline
$x$ & $g(x)$ \\
\hline
0 & 21,989 \\
\hline
2 & 17,811 \\
\hline
4 & 14,427 \\
\hline
6 & 11,686 \\
\hline
\end{tabular}
\][/tex]

The [tex]$\square$[/tex] family's car had the greater initial resale value.
During the first six years, the resale value of the Rivera family's car decreases at an average rate [tex]$\square$[/tex] the resale value of the Patel family's car.



Answer :

GinnyAnswer
Let's carefully compare the information provided to select the correct answers.

1. Initial Resale Value Comparison:

- The Rivera family's car had an initial resale value of [tex]$21,249. - The Patel family's car had an initial resale value of $[/tex]21,989.

Comparing these values:
- [tex]$21,989 > 21,249$[/tex]

Therefore, the Patel family's car had the greater initial resale value.

2. Rate of Decrease Comparison:

First, we verify the average rate of decrease for both families' cars over six years.

- Rivera Family Car:
- Initial value: [tex]$21,249 - Decrease function: $[/tex]21,249 \times (0.88^x)[tex]$ After 6 years: - Final value: $[/tex]21,249 \times (0.88^6) \approx 11,518[tex]$ (not exact but for illustration) - Average rate of decrease = (Initial value - Final value) / Number of years - Average rate of decrease = $[/tex](21,249 - 11,518) / 6 \approx 1,897[tex]$ - Patel Family Car: - Initial value: $[/tex]21,989
- Final value after 6 years: [tex]$11,686 - Average rate of decrease = (Initial value - Final value) / Number of years - Average rate of decrease = $[/tex](21,989 - 11,686) / 6 \approx 1,717[tex]$ Comparing these rates: - $[/tex]1,896.81 > 1,717.17$

Therefore, the resale value of the Rivera family's car decreases at an average rate greater than the resale value of the Patel family's car.

Final Answer:
- The Patel family's car had the greater initial resale value.
- During the first six years, the resale value of the Rivera family's car decreases at an average rate greater than the resale value of the Patel family's car.

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