Final answer:
The value of the car 17 years after it was purchased is $10,000 to the nearest hundred dollars.
Step-by-step explanation:
To find the value of the car 17 years after it was purchased, we need to calculate how many times the value depreciates by 1/2 every three years. Since 17 is not divisible by 3, we need to round down to the nearest multiple of 3, which is 15. Therefore, the value depreciates by half twice: once after 3 years and once after 6 years.
Starting with the initial value of $40,000, the value depreciates by half after 3 years to $40,000/2 = $20,000. Then, after another 3 years, the value depreciates by half again to $20,000/2 = $10,000. From this point, the value remains constant since no further depreciation occurs.
Therefore, the value of the car 17 years after it was purchased is $10,000 to the nearest hundred dollars.