Question

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.

Answer 1

A. The amount of money Aria's car is worth over time is an example of exponential decay because it follows a pattern where it decreases by a fixed percentage each year. The value of her car is being multiplied by the same constant (0.85) each year, resulting in a decreasing value over time.

B. The worth of Aria's car each year for 8 years can be described by the sequence:

$36,000, $30,600, $26,010, $22,109, $18,793, $15,974, $13,578, $11,542