Depreciation
a sports utility vehicle that costs $21,500 new has a book value of $13,600 after 2 years.
(a) find a linear model for the value of the vehicle.
(b) find an exponential model for the value of the vehicle.
(c) find the book values of the vehicle after 1 year and after 4 years using each model.
(d) use a graphing utility to graph the two models in the same viewing window. which model depreciates faster in the first 2 years?
(e) explain the advantages and disadvantages of using eac model to a buyer and to a seller.

a)

b) f(x)

c) Year 1: Linear $17550, exponential $17099

Year 4: Linear $5700, exponential $8601

d) Exponential model

e) The linear model depreciates the value quicker than exponential model long term around 4 years

Step-by-step explanation:

a) At year 0 the price is 21500 and at year 2 the price is 13600

WE can use points (0,21500) and (2,13600)

We can determine the gradient

We can use the point slow formula:

b) We can use the following equation:

f(x)

f(x) is the depreciation value after amount of time t, a is the new value, r is the rate of depreciation and x is the time.

The depreciation rate is 20.47% and is negative because it decreases the new value of the car

c) Year 1:

f(x)

Year 4:

f(x)

d) Year 2

f(x)

step-by-step explanation:

bob the banana