math help!

Question

Nick has been looking for a new car. He decides to buy a small SUV for $35 000. It is known that the SUV will depreciate by 20% of its current value every year.


a) Write an equation to relate the depreciated value, V, of the vehicle to the age, t, in years, of the car.

b) Use the equation to determine the value of the car 2 years after Nick buys it.

c) Approximately how long will it take the car to depreciate to $3000?

Answer 1

Since the car depreciates 20% each year, it is worth 80% of the previous year's value. The equation that shows the depreciated value is

                       A = A₀(.8)^t Therefore after two years the value of the car would be     A = $35,000(.8)² = $22,400. The number of years required for the car to be worth $3,000 can be found by solving the equation

                                $3,000 = $35,000(.8)^t.

Divide both sides by 35,000 to get

                                 .085714 = .8^t    Then take the log of both sides to get            log(.085714) = log(.8)^t = t log(.8)  Now divide both sides by log (.8) to get   t = log(.085714)/log(.8) = 11 years

Answer 2

This can be represented as exponential decreasing function.

y = A(1 - r)t

A = starting amount
r = rate
t = years

y = 35,000(1 - .20)^t

 

y = 35,000(.80)^t

 

The above equation represents the depreciated value of the SUV, after t years

To determine the value after 2 years,  substitute 2 for t

 

   y = 35,000(.80)²

      = 35,000(.64)

      = 22,400

 

The vehicle will be worth $22,400 after 2 years

 

To find out how long it will take for the vehicle to depreciate to 3,000, substitute 3,000 for y and solve for t.

 

   3000 = 35,000(.80)^t

 

I made a mistake when computing this earlier ... the other tutors calculation is correct.