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.

Create a sequence that describes the worth of Aria's car each year for 8 years.
$__, $__, $__, $__, $__, $__, $__, $__

Create a formula for the worth of Aria's car over time.
y = a * b^x

a = initial amount
b = growth factor

y = __(__)^x

Use your formula and find how much Aria's car is worth in 20 years.
After 20 years, Aria's car is worth $_______

Answer 1

Sequence for 8 years (year 0 through year 7):
$36,000, $30,600, $26,010, $22,108.50, $18,792.23, $15,972.39, $13,576.53, $11,540.06

Exponential formula:
y = 36000(0.85)^x, where x = years after purchase

Value after 20 years:
y = 36000(0.85)^20 ≈ $1,395.35