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Suppose that a company has just purchased a new computer for \( \$ 3000 \). The company chooses to depreciate using the straight-line method for 5 years. (a) Write a linear function that expresses the book value of the computer as a function of its age. \( \mathrm{V}(\mathrm{x})=\square \) (Type your answer in slope-intercept form.)

Ask by French George. in the United States
Mar 13,2025

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The book value \( V(x) \) of the computer after \( x \) years is given by: \[ V(x) = 3000 - 600x \]

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The straight-line depreciation method means that the value of the computer decreases by the same amount each year. The total depreciation over 5 years for a \$3000 computer is \( \frac{3000}{5} = 600 \) dollars per year. Thus, the function that describes the book value \( V(x) \) of the computer as a function of its age \( x \) (in years) is: \[ V(x) = 3000 - 600x \] Now you've got the book value linear function! Keep it in mind as companies often need these calculations for their financial statements. In the realm of business, understanding depreciation is critical! Not only does it affect financial reporting, but it also impacts tax deductions. Companies can deduct depreciation from taxable income, which means less bucks will be going to Uncle Sam! So, knowing this straight-line method can save some serious cash in the long run.

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