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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

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  • 1 month ago

    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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