Final answer:
To calculate the value of a car after two years with a 13% annual depreciation rate from an initial value of $9,000, you apply the exponential decay formula, resulting in an estimated future value of $6,811.70.
Step-by-step explanation:
The question is asking for the future value of a car that is depreciating at a rate of 13% per year. Given the current value of the car is $9,000, we can find the car's value after two years by applying the formula for exponential decay, which is:
Future Value = Present Value × (1 - rate of depreciation)^number of years.
In this case,
Future Value = $9,000 × (1 - 0.13)^2.
Calculating this, we get:
Future Value = $9,000 × 0.87^2
Future Value = $9,000 × 0.7569
Future Value = $6,811.70 (rounded to two decimal places).
Therefore, the car will be worth approximately $6,811.70 in two years if it continues to depreciate at the same rate.