The value of a car decreases at a constant rate. After 3 years the value of the car is $15,000. After 2 more years the value of the car is $

Question

The value of a car decreases at a constant rate. After 3 years the value of the car is $15,000. After 2 more years the value of the car is $11,000. Write and solve a linear equation to find the value of the car after 8 years.

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Kaylee 2 weeks 2021-10-13T03:20:30+00:00 1 Answer 0

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    2021-10-13T03:22:22+00:00

    Answer:

    The Linear equation: V (x) =  21,000 – 2000x

    Where V = Value of Car after a time period ($)

                x = Number of years (yrs)

    Value of Car after 8 years = $5,000

    Step-by-step explanation:

    Let the value of the car and the number of years be related by the Linear equation :

    V(x) = Mx +C——————————————– (1)

    Where V =Value of Car after a time period ($)

               x  = Number of years (yrs)

               M = Slope of the linear relationship

               C = The intercept of the straight line on the value axis

    From the question two different coordinates of Value and the number of years where given: (V₁ ,x₁)  and (V₂ ,x₂)

    First coordinate (V₁ ,x₁)  = ($15,000 , 3)

    Second coordinate (V₂ ,x₂)  = ($11,000, 5)

    These can be substituted into equation (1) and (2) to calculate the for M & C

    Substituting the first coordinate into (1) we have :

    15,000 =  3M +C—————————————————————–(2)

    Substituting the second coordinate into (1) we have :

    11,000 = 5M +C——————————————————————(3)

    Solving equation  (2) and (3) simultaneously using elimination method, we have:

    15,000 =  3M +C

    11,000 = 5M +C

    4000 = -2M

    M = -2000

    Substituting the value of M into equation (3) we have:

    11,000 = 5M +C

    11,000 = 5(-2000) +C

    11,000 = -10,000 +C

    C =21,000

    Substituting the value of M and  C into equation (1), we have the Linear relationship for Value  and the number of years

    V (x) = -2000x + 21,000—————————————————————- (4)

    V (x) =  21,000 – 2000x —————————————————————- (5)

    Substituting x = 8 years into equation (5) we have:

    V (x) =  21,000 – 2000x

           = 21000 – 2000 (8)

           = 21000 – 16000

           = $5000

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