Question

The value of car after it is purchased depreciates according to the formula Vn=250000.85n, where V(n) is the car’ value in the nth year after it was purchased.

What is the purchased price of the car?
What is the annual rate of depreciation?
How much value does it lose in its fifth year?
After how many years will the value of the car be half of the original purchased price?

Answer 1

25000

0.15

−1957.523

Explanation:

Given the function :

Vn=250000.85n

Value of car due to Depreciation,

V(n) value of car after n years.

Initial value of car ; value of car at year 0

V(0) = Vn=25000(0.85)^(0)

V(0) = 25000(0.85)^0

V(0) = 25000(1)

V(0) = 25000

The Decay rate = annual Depreciation

According the exponential function.

mb^n

m = initial value

b = 1 - Decay rate

Relating to the equation given :

b = 0.85

0.85 = 1 - Decay rate

Decay rate = 1 - 0.85

Decay rate = 0.15

Value lost in fifth year : V(5) - V(4)

n = 5

V(5) = 25000(0.85)^5

V(5) = 25000 * 0.4437053125

V(5) = 11092.6328125

V(4) = 25000(0.85)^4 = 13050.15625

11092.6328125 - 13050.15625

= −1957.523