An equation for the depreciation of a car is given by y = a(1 – r)t , where y = current value of the car, a = original cost, r = rate of depreciation, and t = time, in years. the value of a car is half what it originally cost. the rate of depreciation is 10%. approximately how old is the car?

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).

your answer is d 2,500

step-by-step explanation: