Final answer:
a) The straight line depreciation equation is Value = Original Value - (Depreciation Rate × Years), where Depreciation Rate = Original Value / Years. b) It will take 6.5 years for the car to be worth half its value. c) It will take 9.1 years for the car to be worth $10,000.
Step-by-step explanation:
a.) The straight line depreciation equation can be written as: Value = Original Value - (Depreciation Rate × Years). Since the car takes 13 years to totally depreciate, the depreciation rate can be found by dividing the original value by the number of years: Depreciation Rate = Original Value / Years. Substituting the values, we get: Value = $34,450 - ($34,450 / 13) × Years.
b.) To find how long it will take for the car to be worth half its value, we set the value equal to half the original value and solve for Years: Value = $34,450 / 2. Solving the equation, we get Years = 13 / 2 = 6.5 years.
c.) To find how long it will take for the car to be worth $10,000, we set the value equal to $10,000 and solve for Years: $10,000 = $34,450 - ($34,450 / 13) × Years. Solving the equation, we get Years = 9.1 years.