Question

A new car was valued at $28,000, and it's value depreciated to $14,000 over the next 3 years. Use the exponential equation for depreciation to answer the following questions. A) What was the annual percent rate of depreciation, to 2 decimal places? Your answer will be a positive number. r r = %. B) Assume that the car value continues to drop by the same percentage. What will the value of the car be when the car is 10 years old? value = $ Round to the nearest dollar.

Answer 1

The exponential equation (in thousands) is:
$V = 28 e^{-rt}$
plug in t=3 yrs, and solve for 'r'.
$14 = 28 e^{-3r} \\ \\ \frac{1}{2} = e^{-3r} \\ \\ ln(\frac{1}{2}) = -3r \\ \\ r = \frac{ln(\frac{1}{2})}{-3} = 0.231 = 23.1%$

Find value of car when t = 10
$V = 28e^{-2.31} = 2.779$