Final answer:
The value of the motorcycle in 2025 can be calculated using the exponential decay formula, which after the calculation shows the motorcycle will be worth approximately $8,286.35.
Step-by-step explanation:
To calculate the value of the motorcycle in 2025 after depreciating 5% each year, we can use the formula for exponential decay V = P(1 - r)^n, where:
V is the future value of the motorcycle,
P is the initial value ($13,000 in this case),
r is the annual depreciation rate (5% or 0.05),
n is the number of years (2025 - 2015 = 10 years).
Plugging the values into the formula, we get:
V = $13,000(1 - 0.05)^10
Calculating this yields:
V = $13,000(0.95)^10
V ≈ $8,286.35
Therefore, the motorcycle will be worth approximately $8,286.35 in 2025 after depreciating 5% annually for 10 years.