Final answer:
The value of the motorcycle after 7 years with a continuous depreciation rate of 9% per annum is approximately $5,303.
Step-by-step explanation:
To calculate the value of a motorcycle after 7 years with a continuous depreciation of 9% per annum, we use the formula for continuous depreciation, which is P(t) = P0 * e-rt, where P(t) is the future value, P0 is the initial value, r is the rate of depreciation, and t is the time in years.
The motorcycle's initial value is $10,000. Therefore, P0 = $10,000, r = 0.09 (since 9% is 0.09 as a decimal), and t = 7 years. Plugging these values into the formula gives:
P(7) = $10,000 * e-(0.09*7) ≈ $10,000 * e-0.63 ≈ $10,000 * 0.5303 ≈ $5,303
So, the motorcycle's value after 7 years is approximately $5,303.