Aria buys a new car for $36,000. She learns that every year her car will depreciate in value by 15%. This means that each year her car will be worth 85% of what it was the previous year. Aria tracks how much her car is worth over time.
A. Explain how the amount of money Aria's car is worth over time is an example of exponential decay
B. Create a sequence that describes the worth of Aria's car each year for 8 years.
A. The amount of money Aria's car is worth over time is an example of exponential decay because the car's value decreases by a fixed percentage (15% or 0.15) each year. Exponential decay occurs when a quantity decreases at a constant rate over time, and in this case, the car's value decreases at a rate of 15% annually.
B. To create a sequence that describes the worth of Aria's car each year for 8 years, we can start with the initial value of $36,000 and multiply it by 0.85 (1 - 0.15) for each subsequent year:
Year 1: $36,000 * 0.85 = $30,600
Year 2: $30,600 * 0.85 = $26,010
Year 3: $26,010 * 0.85 = $22,108.50
Year 4: $22,108.50 * 0.85 = $18,792.23
Year 5: $18,792.23 * 0.85 = $15,973.90
Year 6: $15,973.90 * 0.85 = $13,677.82
Year 7: $13,677.82 * 0.85 = $11,626.15
Year 8: $11,626.15 * 0.85 = $9,882.23
So, the sequence representing the worth of Aria's car each year for 8 years would be:
$36,000, $30,600, $26,010, $22,108.50, $18,792.23, $15,973.90, $13,677.82, $11,626.15, $9,882.23.