Answer :
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 = [tex]\frac{x}{2}[/tex]
So, value of car after depreciation in another 4 years = Half of the value after 4 years = [tex]\frac{1}{2}(\frac{x}{2})=\frac{x}{4}[/tex]
Therefore, final depreciated value after 8 years is [tex]\frac{x}{4}[/tex].
But, as per question, final depreciated value is $5000. Thus,
[tex]\frac{x}{4}=5000\\x=5000\times 4\\x=20000[/tex]
Therefore, the original price of the car was $20,000.