Question

BusiNESS-DEPRECIATION A copy machine was purchased by a law firm for $\$ 8,000$ and is assumed to have a depreciated value of $\$ 0$ after 5 years. The firm takes straight-line depreciation over the 5 -year period. (A) Find a linear equation that expresses value $V$ in dollars in terms of time $t$ in years. (B) What is the depreciated value after 3 years? (C) What is the slope of the graph of the equation found in part A? Interpret verbally.

Name: Problem 93, Chapter 2: Precalculus: Graphs and Models
Uploaded: 2023-10-27T04:49:13-08:00
Duration: 2 min 21 s
Channel: Khushbu Rani

    BusiNESS-DEPRECIATION A copy machine was purchased by a law firm for $\$ 8,000$ and is assumed to have a depreciated value of $\$ 0$ after 5 years. The firm takes straight-line depreciation over the 5 -year period.
(A) Find a linear equation that expresses value $V$ in dollars in terms of time $t$ in years.
(B) What is the depreciated value after 3 years?
(C) What is the slope of the graph of the equation found in part A? Interpret verbally.

Precalculus: Graphs and Models

Raymond A. Barnett,… 3rd Edition

Chapter 2, Problem 93

Instant Answer

Solved by Expert Khushbu Rani

10/27/2023

Step 1

We know that the machine was purchased for $8000 and after 5 years, its value is $0. We can use these two points, (0,8000) and (5,0), to find the slope. The formula for the slope is (y2-y1)/(x2-x1). Substituting the given points into the formula, we get: \[ m = Show more…

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BusiNESS-DEPRECIATION A copy machine was purchased by a law firm for $\$ 8,000$ and is assumed to have a depreciated value of $\$ 0$ after 5 years. The firm takes straight-line depreciation over the 5 -year period. (A) Find a linear equation that expresses value $V$ in dollars in terms of time $t$ in years. (B) What is the depreciated value after 3 years? (C) What is the slope of the graph of the equation found in part A? Interpret verbally.

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Key Concepts

Straight-line Depreciation

Straight-line depreciation is a method of allocating the cost of an asset evenly over its useful life. It assumes that the asset's value decreases by the same fixed amount each year, leading to a uniform reduction in value over time.

Linear Equations

Linear equations are used to model relationships where one variable changes at a constant rate with respect to another. In depreciation problems, a linear equation represents how the value of an asset decreases over time with a constant rate of change.

Slope

The slope in a linear equation indicates the rate of change of the dependent variable relative to the independent variable. For straight-line depreciation, the slope represents the amount by which the asset's value decreases each year.

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