Question

Independent: The value of an automobile bought in 2006 continues to decrease as time passes. This is

called depreciation. Two years after the car was bought, it was worth $17,500; four years after it was
bought, it was worth $14,800, Write a linear equation to describe the relationship between value of an
automobile Y after so many years X (after time of purchase). Use this equation to estimate the value of
the same automobile in 2012.

Answer 1

So we have this data:

- After 2 years, it's worth 17500$

- After 4 years, it's worth 14800$

Let's see how much decreases per year:

4 - 2 = 2 years difference

17500 - 14800 = 2700$ difference

2700$ / 2y = 1350$/y (amount the value of the car decreases per year)

Now we find how much it was worth at the beginning, for this we add 1350$ twice (for the 2 years) to 17500 (the amount it was worth 2 years after it was bought):

17500 + 2 * 1350 = 20200$

Our equation, then:

Y = 20200 - 1350X

For 2012 (6 years after 2006, the year it was bought):

Y = 20200 - 1350 * 6 = 20200 - 8100 = 12100$