Suppose that a company has just purchased a new computer for $1100. The company chooses to depreciate using the straight-line method for 3 years.
(a) Write a linear function that expresses the book value V of the computer as a function of its age x.
(b) What is the domain of the function found in part (a)?
(c) Graph the linear function.
(d) What is the book value of the computer after 2 years?
(e) When will the computer have a book value of $300
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(a) The book value V of the computer decreases linearly from $1100 to $0 over 3 years. This can be expressed as a linear function V(x) = 1100 - 1100/3*x, where x is the age of the computer in years.
(b) The domain of the function is 0 ≤ x ≤ 3, since the computer's age can't be less than 0 or more than 3 years.
(c) The graph of the function is a straight line that starts at (0, 1100) and ends at (3, 0).
(d) The book value of the computer after 2 years is V(2) = 1100 - 1100/3*2 = $733.33.
(e) The computer will have a book value of $300 when V(x) = 300. Solving the equation 1100 - 1100/3*x = 300 gives x = 2.4 years.
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