Answer:
The value of the car depreciates according to an exponential decay model. To find the value of the car when it was new, we can use the formula for exponential decay: V = V0 * e^(-rt) where V is the current value of the car, V0 is the initial value of the car (when it was new), e is the base of the natural logarithm (approximately 2.718), r is the rate of depreciation per year (expressed as a decimal), and t is the number of years. We are given that the value of the car is $12,000 at the end of 5 years and that its value has been decreasing at a rate of 9% per year. We can convert the rate to a decimal by dividing it by 100: 9% = 0.09. Substituting the given values into the formula, we have: 12,000 = V0 * e^(-0.09 * 5) To solve for V0, we need to isolate it on one side of the equation. We can divide both sides of the equation by e^(-0.09 * 5): V0 = 12,000 / e^(-0.09 * 5) Using a calculator or a math tool, we can find that e^(-0.09 * 5) is approximately 0.6772. Dividing 12,000 by 0.6772, we find that the value of the car when it was new (V0) is approximately $17,725.19. Therefore, the value of the car when it was new is approximately $17,725.19.
Explanation: