Final answer:
To find the value of David's car after 10 years of continuous depreciation at a rate of 6%, the exponential decay formula is used. After the calculation, the car's value in 2017 is approximately $20,467.33.
Step-by-step explanation:
The student's question involves calculating the depreciation of David's car over a 10-year period with a constant annual depreciation rate. To solve this problem, we will use the formula for exponential decay, which is V = P(1 - r)^t, where:
- V is the future value of the car.
- P is the present value or the initial value of the car, which is $38,000.
- r is the depreciation rate per period, which is 6% or 0.06.
- t is the number of time periods the car has been depreciating, which is 10 years from 2007 to 2017.
By substituting the given values into the formula, we get:
V = $38,000 × (1 - 0.06)^{10}
Let's calculate the future value:
V = $38,000 × (0.94)^{10}
V = $38,000 × (0.538614)
V = $20,467.33
Therefore, the value of David's car in 2017, after continuous depreciation, would be approximately $20,467.33.