Answer:
Original price of car = $20,000
Step-by-step explanation:
Let the original price of the car be 'x' dollars.
Given:
Here, the depreciation of the car is occuring exponentially as the value depreciates to half in every four years.
Worth of car after 8 years = $5000
Value after depreciation in 4 years = Half of original value = ![\frac{x}{2}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B2%7D)
So, value of car after depreciation in another 4 years = Half of the value after 4 years = ![\frac{1}{2}(\frac{x}{2})=\frac{x}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%28%5Cfrac%7Bx%7D%7B2%7D%29%3D%5Cfrac%7Bx%7D%7B4%7D)
Therefore, final depreciated value after 8 years is
.
But, as per question, final depreciated value is $5000. Thus,
![\frac{x}{4}=5000\\x=5000\times 4\\x=20000](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B4%7D%3D5000%5C%5Cx%3D5000%5Ctimes%204%5C%5Cx%3D20000)
Therefore, the original price of the car was $20,000.