Final answer:
To calculate the approximate value of Mark's car in 2025, we use the exponential decay formula similar to compound interest, with an initial value of $35,000 and an 8% annual depreciation rate over 7 years, resulting in an approximate value of $17,542.
Step-by-step explanation:
The depreciation of a car is a mathematical concept that can be calculated using the exponential decay formula, which is similar in structure to the compound interest formula. In this finance-related mathematics problem, Mark wants to know the approximate value of the car in 2025 given that the car was purchased for $35,000 in 2018 and depreciates at a rate of 8% each year.
To solve this, we use the formula A = a(1 - r)^t, where:
- A is the amount of money that remains after depreciation.
- a is the initial amount which is $35,000 in this case.
- r is the rate of depreciation per period which is 8% or 0.08 as a decimal.
- t is the number of time periods for the depreciation which is the number of years from 2018 to 2025, equal to 7 years.
Now we can perform the calculation:
A = 35000(1 - 0.08)^7A = 35000(1 - 0.08)^7A = 35000(0.92)^7A = 35000(0.5012)A ≈ $17,542
So, the approximate value of the car in 2025 is $17,542.