Final answer:
The value of the car 17 years after it was purchased is $600 ( 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 determine the depreciation rate.
The car depreciates by one half every 4 years, which means its value is reduced by half after every 4-year period.
Since 17 is not a multiple of 4, we need to divide it by 4 to determine the number of 4-year periods. 17 divided by 4 is 4 with a remainder of 1.
The car will undergo 4 complete 4-year periods of depreciation, reducing its value to half after each period. The initial value of the car is $18,000.
After 4 years, the value becomes $18,000 / 2 = $9,000.
After another 4 years, the value becomes $9,000 / 2 = $4,500.
After the third 4-year period, the value becomes $4,500 / 2 = $2,250.
After the fourth 4-year period, the value becomes $2,250 / 2 = $1,125.
After the 4 complete 4-year periods, there is still 1 year remaining.
The car will depreciate by half in this remaining year, reducing its value to $1,125 / 2 = $562.50.
To find the value to the nearest hundred dollars, we round $562.50 to the nearest hundred, which is $600.