From the depreciation formula:

we know the final value A=$11,000, the initial values P=$38000 and the number of years n=6. Then, we need to find the rate r. By substituting these values into the formula, we have

Then, by dividing both sides by 38000, we get

Now, by applying 6th root to both sides, we have

by subtracting 1 to both sides, we have

or equivalently,

Then, the rate is given by

Once we know the rate, we can find the car's value by 2017. Then, we have

where n=10 years (from 2007 to 2017). By computing the term into the paranthesis, we have

which gives

Therefore, the answer is $4813.549