Aria buys a new car for $36000 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 was the previous year aria tracks how much her car is worth over time
C. Create a formula for the worth of arias car over time
Y=a×b^x
A= initial amount
B= growth factor
D. Use your formula in C and find how much arias car is worth in 20 years
To create the formula for the worth of Aria's car over time, we can use the formula:
Y = A * (1 - r)^x
Where:
Y = worth of the car after x years
A = initial amount (purchase price of the car)
r = depreciation rate per year (expressed as a decimal)
x = number of years
In this case, Aria's car depreciates by 15% each year, which means the depreciation rate (r) is 0.15. Therefore, the formula becomes:
Y = 36000 * (1 - 0.15)^x
To find how much Aria's car is worth in 20 years, we substitute x = 20 into the formula:
Y = 36000 * (1 - 0.15)^20
Y = 36000 * (0.85)^20
Y ≈ 3621.47
Therefore, Aria's car will be worth approximately $3621.47 in 20 years.