Question

A new car is purchased for $18,000, and over time its value depreciates by one-half every 4 years. What is the value of the car 17 years after it was purchased, to the nearest hundred dollars?

Answer 1

The value of the car 17 years after it was purchased, given the depreciation rate of halving every 4 years, is approximately $1,100 when rounded to the nearest hundred dollars.

Step-by-step explanation:

The question involves calculating the depreciated value of a car over time, which is a concept in Mathematics, specifically involving exponential decay. The car's initial purchase price is $18,000 and it depreciates to half its value every 4 years. To find the value of the car after 17 years, we need to determine how many 4-year intervals fit into 17 years and then apply the depreciation accordingly.

To do this, we divide 17 by 4, which gives us 4 full intervals with 1 year left over. After each 4-year interval, the car's value is halved. Therefore, after 16 years (4 intervals), we'd have:

1. After 4 years, the value would be $18,000 / 2 = $9,000.
2. After 8 years, the value would be $9,000 / 2 = $4,500.
3. After 12 years, the value would be $4,500 / 2 = $2,250.
4. After 16 years, the value would be $2,250 / 2 = $1,125.

Since the car does not depreciate during the last remaining year, the car's value after 17 years is approximately $1,100 when rounded to the nearest hundred dollars, as the depreciation occurs every 4 years and not continuously.