Answer:
The car is 6.5788 years old.
Step-by-step explanation:
The key to solve the problem is in the following sentence: "The value of a car is half what it originally cost". Keep in mind that is the current value and is the original cost. It means that is half of : .
It is assumed that the rate of depreciation is annually and its value is . Remember that equals , so .
For finding the value of , you must replace the values of and in the depreciation formula:
After cancelling the variable the equation would be:
For finding the value of you must apply natural algorithm in both sides:
The previous value can be split in two parts: . The first part refers to years and the second part can be converted to months by multiplying the total months in a year () by .
Thus, the car is 6.5788 years old (which is approximately 6 years and almost 7 months).