Cassandra bought a car for 22,385. The value depreciates 14% a year.
a. Write a function, d(x), that gives the value of the car after x years.
b. What will the value of Cassandra's car be after 10 years
a. V = C - C*(1-r)^t.
V = Value.
C = Cost.
r = Depreciation rate.
T = Time in years.
b. V = 22,385(0.86)^10 =
a. Correction: V = C(1-r)^t.
a. To write a function that gives the value of the car after x years, we need to apply the depreciation rate to the initial value of the car for each year.
The formula to calculate the value after x years is:
Value after x years = Initial value * (1 - Depreciation rate)^x
In this case, the initial value is $22,385 and the depreciation rate is 14% or 0.14 (since it is given as a decimal). So the function d(x) can be written as:
d(x) = 22,385 * (1 - 0.14)^x
b. To find the value of Cassandra's car after 10 years, we need to substitute x = 10 into the function d(x):
d(10) = 22,385 * (1 - 0.14)^10
To calculate this value, you can follow these steps:
1. Subtract the depreciation rate from 1: 1 - 0.14 = 0.86
2. Raise 0.86 to the power of 10: 0.86^10 ≈ 0.1967151357
3. Multiply this result by the initial value: 22,385 * 0.1967151357 ≈ 4,395.11
Therefore, the value of Cassandra's car after 10 years will be approximately $4,395.11.