Depreciation. A small business buys a computer for 4000 ....

Depreciation. A small business buys a computer for $\$ 4000 .$ After 4 years the value of the computer is expected to be $\$ 200$ . For accounting purposes the business uses linear depreciation to assess the value of the computer at a given time. This means that if $V$ is the value of the computer at time $t,$ then a linear equation is used to relate $V$ and $t .$ \begin{equation}\begin{array}{l}{\text { (a) Find a linear equation that relates } V \text { and } t} \\ {\text { (b) Sketch a graph of this linear equation. }} \\ {\text { (c) What do the slope and } V \text { -intercept of the graph }} \\ {\text { represent? }} \\ {\text { (d) Find the depreciated value of the computer 3 years from }} \\ {\text { the date of purchase. }}\end{array}\end{equation}

Depreciation. A small business buys a computer for $\$ 4000 .$ After 4 years the value of the computer is expected to be $\$ 200$ . For accounting purposes the business uses linear depreciation to assess the value of the computer at a given time. This means that if $V$ is the value of the computer at time $t,$ then a linear equation is used to relate $V$ and $t .$
\begin{equation}\begin{array}{l}{\text { (a) Find a linear equation that relates } V \text { and } t} \\ {\text { (b) Sketch a graph of this linear equation. }} \\ {\text { (c) What do the slope and } V \text { -intercept of the graph }} \\ {\text { represent? }} \\ {\text { (d) Find the depreciated value of the computer 3 years from }} \\ {\text { the date of purchase. }}\end{array}\end{equation}

Key Concepts

Linear Depreciation

Linear depreciation is an accounting method used to allocate the cost of a tangible asset evenly over its useful life. This means that the asset’s value decreases by a constant amount each period, making calculations straightforward and predictable for financial and tax purposes.

Linear Equation in Slope-Intercept Form

A linear equation expressed in the slope-intercept form (y = mx + b) is a mathematical model that describes a straight-line relationship between two variables. In this context, it is used to relate the value of an asset to time, where the constant rate of depreciation is represented by the slope and the initial value of the asset is given by the y-intercept.

Interpretation of the Slope

In a depreciation model, the slope represents the amount by which the asset’s value declines per unit of time. A negative slope indicates a decrease in value over time, quantifying the loss of value over each time period, which is essential for understanding how quickly an asset depreciates.

Interpretation of the Y-Intercept

The y-intercept in a linear depreciation equation indicates the initial value of the asset at the beginning of the depreciation period. It represents the value of the asset when time is zero, serving as the starting point for the depreciation calculation.

Graphical Representation of Linear Relationships

Graphing a linear depreciation equation results in a straight line that visually illustrates the asset's declining value over time. The graph typically features the initial value at time zero and a steady decline, making it easier to predict future values and to understand the rate of depreciation.

Calculation of Depreciated Value

Calculating the depreciated value involves substituting the desired time into the linear depreciation equation. This process yields the current estimated value of the asset based on its constant rate of depreciation, enabling informed financial decision-making and accounting adjustments.

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