Car Depreciation Over Time

The value of a new car in 2015 was $40,000. It depreciates 7% each year. How much will the car be worth in 2024?

Understanding how depreciation works is crucial in evaluating the long-term value of any asset, such as a car. Depreciation is a financial concept that represents the loss of asset value over time. It is a common practice to calculate depreciation to understand how an asset's value changes each year and to project its worth in the future. This problem is a practical example of applying exponential decay, where the value of the asset decreases by a fixed percentage annually.

To approach this problem, consider the car's initial value and recognize that each year it decreases by a percentage of its value from the previous year. This forms a geometric sequence, where each term is 93% of the previous one (100% - 7% depreciation). The problem involves understanding the geometric nature of the situation—recognizing it is a form of exponential decay—and applying this to find the car's value over a defined number of years. Observing how changes in the percentage can affect the total value over the years is crucial, and this understanding can be applied in various real-world contexts beyond cars, such as technology products, equipment, or even financial forecasts.

Through this problem, students can practice geometric progression calculation and develop a better understanding of how initial values decrease exponentially over time. This concept is not only relevant in mathematics but also widely applicable in fields like economics, finance, and IT asset management, offering a valuable interdisciplinary perspective.