Final answer:
The initial value of the car is $27,500, and its value after 11 years, calculated using the given depreciation function and rounding to the nearest dollar, is $6,005.
Step-by-step explanation:
The question asks for the initial value of a car and its value after 11 years, given the depreciation function v(t) = 27,500 (0.84)^t.
To find the initial value of the car, we evaluate the function at t = 0, which gives us:
v(0) = 27,500 (0.84)^0 = 27,500 (1) = $27,500.
This means the initial value of the car is $27,500.
To find the value after 11 years, we substitute t = 11 into the function:
v(11) = 27,500 (0.84)^11 = $6,004.76.
After rounding to the nearest dollar, the car's value after 11 years is $6,005.