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V (t) = 27,500 (0.84)^t

Find the initial value of the car and the value after 11 years.
Round your answers to the nearest dollar as necessary.

User Bizl
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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.

User David Vasandani
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