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# A 2005 Jeep Wrangler that costs \$30,788 now has a book value of \$18,000 after 2 years?

a) Find the linear model V=mt+b

b) Find the exponential model V=ae^kt

c) find the book values of the vehicle after 1 year and after 3 years using each model

d) Explain the pros and cons of using each model to a buyer and a seller

### 1 Answer

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• a) V=mt+b in 2005

V= 30788

t= 0

V=mt+b

30788= m*0 + b

b= 30788

in 2007

V = 18000

t =2

V=mt+b

18000 = m2 + 30788

m2 = -12788

m = - 6394

Hence,the linear model is V= -6394t + 30788

b) Find the exponential model V=ae^kt

V= 30788

t = 0

V=ae^kt

30788 = ae^k0

30788 = a

In 2007

V = 18000

t=0

V=ae^kt

18000 = 30788e^2k

log(18000/30788) = 2k

-116 = k

Hence,the exponential model is V = 30788e^-116k

c) find the book values of the vehicle after 1 year and after 3 years using each model

Using lineal model to calculate value after 1 year we put t =1 in lineal model

V= -6394t + 30788

V= -6394+ 30788

V = 24394

Using lineal model to calculate value after 3 year we put t =3 in lineal model

V= -6394t + 30788

V= -6394 x 3 + 30788

V = -19182 + 30788

V = 1606

Using lineal exponential to calculate value after 1 year we put t =1 in lineal exponential model.

V = 30788e^-116k

V = 30788e^-116

V = 30788 x .890

V = 27415

Using lineal exponential to calculate value after 3 year we put t =3 in lineal exponential model.

V = 30788e^-116k

V = 30788e^-116*3

V = 30788 x .705

V = 21717

d) Explain the pros and cons of using each model to a buyer and a seller

These models are useful both buyer and seller to calculate the value of product after some time.

I hope this helps you!!

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