Question

A new car is purchased for $16,000. The value of the car depreciates at 7.5% per year. To the nearest tenth of a year, how long will it be until the value of the car is $6,900?

A. 4.2 years

B. 5.6 years

C. 7.8 years

D. 9.3 years

Answer 1

To find out how long it will take for the value of the car to reach $6,900, we need to determine the number of years it takes for the car's value to depreciate from $16,000 to $6,900. The car depreciates at a rate of 7.5% per year. Using the formula for exponential decay, we find that it will take approximately 5.6 years for the value of the car to reach $6,900.

Step-by-step explanation:

To find out how long it will take for the value of the car to reach $6,900, we need to determine the number of years it takes for the car's value to depreciate from $16,000 to $6,900. The car depreciates at a rate of 7.5% per year. We can use the formula for exponential decay: V = A(1 - r)^t, where V is the final value, A is the initial value, r is the rate of decay as a decimal, and t is the time in years. Plugging in the values, we have 6900 = 16000(1 - 0.075)^t. Rearranging the equation, we get (1 - 0.075)^t = 6900/16000 = 0.43125. Taking the logarithm of both sides, we find t = log(0.43125)/log(0.925), which is approximately equal to 5.556. Therefore, it will take approximately 5.6 years for the value of the car to reach $6,900.