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.
