234k views
3 votes
Rich is comparing the cost of maintaing his car with the depreciating value of the car. When will the cost and value be the same

User Dbugger
by
3.4k points

1 Answer

3 votes

Complete question:

Rich is comparing the cost of maintaining his car with the depreciation value of the car.

The value starts at $20,000 and decreases by 15% each year. The maintanance cost is $500 the first year and increases by 28% per year.

When will the maintenance cost and the value be the same.

Answer:

9 years

Explanation:

Depreciation is modeled by an exponential function :

A = p(1 - r)^t [decrease, '-']

A = 20,000(1 - 0.15)^t

A = 20000(0.85)^t - - - (1)

Maintainace cost :

A = p(1 + r)^t ; [increase, '+']

A = 500(1 + 0.28)^t

A = 500(1.28)^t - - - (2)

Equating (1) and 2

20000(0.85)^t = 500(1.28)^t

1.28^t / 0.85^t = 20000/500

(1.28 / 0.85)^t = 40

Take log of both sides

Log (1.28 / 0.85)^t = log 40

t * 0.1777910 = 1.6020599

t = 1.6020599 / 0.1777910

t = 9.01

t = 9 years

User Vlee
by
3.0k points