For assets such as machines, whose market values drop rapidly in the early years of of usage, businesses often use the double declining-balance method. In practice, a business firm normally employs the double declining- balance method for depreciating such assets for a certain number of years and then switches over to the linear method. The double-declining formula is V(n) = C(1-(2/n))^n where C is the initial value of the assest in dollars, V(n) denotes the book value of the assets at the end of n years, and N is the number of years over which the asset is depreciated A tractor purchased at a cost of $40,000is to depreciated by the double declining balance method over 10 years . (a) What is the book value of the tractor at the end of 3 years? (b) What is the relative rate of change of the book value of the tractor at the end of 3 years?

Linear Algebra: A Modern Introduction
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Author:David Poole
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Chapter2: Systems Of Linear Equations
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For assets such as machines, whose market values drop rapidly in the early years of of usage, businesses often use the double declining-balance method. In practice, a business firm normally employs the double declining- balance method for depreciating such assets for a certain number of years and then switches over to the linear method. The double-declining formula is

V(n) = C(1-(2/n))^n

where C is the initial value of the assest in dollars, V(n) denotes the book value of the assets at the end of n years, and N is the number of years over which the asset is depreciated

A tractor purchased at a cost of $40,000is to depreciated by the double declining balance method over 10 years .

(a) What is the book value of the tractor at the end of 3 years?

(b) What is the relative rate of change of the book value of the tractor at the end of 3 years?

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