An equation for the depreciation of a car is given by y is equal to cap A times open paren 1 minus r close paren to the t th power , where y is equal to current value of the car, cap A is equal to original cost, r is equal to rate of depreciation, and t is equal to time, in years. The value of a car is half what it originally cost. The rate of depreciation is 10 percent Approximately how old is the car?
Since the car is worth half its original cost, y/A = 0.5. Substitute the 10% depreciation rate into the model: 0.5 = (1 - 0.10)^t = 0.9^t, so t = ln(0.5)/ln(0.9) ≈ 6.6 years. The car is approximately 6.6 years old, which is choice A.
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