Straight-line Depreciation Suppose that a company has just...

Straight-line Depreciation Suppose that a company has just purchased a new computer for $\$ 3000 .$ The company chooses to depreciate the computer using the straight-line method over 3 years. (a) Write a linear model that expresses the book value $V$ of the computer as a function of its age $x$ (b) What is the implied 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 $\$ 2000 ?$

Straight-line Depreciation Suppose that a company has just purchased a new computer for $\$ 3000 .$ The company chooses to depreciate the computer using the straight-line method over 3 years.
(a) Write a linear model that expresses the book value $V$ of the computer as a function of its age $x$
(b) What is the implied 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 $\$ 2000 ?$

Key Concepts

Solving Linear Equations

Solving linear equations is a fundamental algebraic process used to find unknown values within the linear model. In depreciation problems, this technique is utilized to determine specific values such as the asset's book value at a given time or the time at which the asset will reach a predetermined book value.

Domain of a Function

The domain of a function encompasses all possible input values for which the function is defined. For a depreciation model, the domain is typically restricted to a specific time interval starting from when the asset is new (time zero) up to the end of its useful life, reflecting the period over which depreciation occurs.

Graphing Linear Functions

Graphing a linear function involves plotting the initial value at time zero (the y-intercept) and using the slope to determine how the value changes over time. This visual representation helps in understanding the consistent decrease in the asset’s value and in identifying key points such as when the asset reaches a particular value.

Linear Models

A linear model is a mathematical representation that depicts a constant rate of change between two variables, typically using a linear equation. In depreciation contexts, the model expresses the asset's value as a function of time, capturing the steady decline in value over the asset's lifespan.

Straight-Line Depreciation

Straight-line depreciation is a method of allocating the cost of an asset evenly over its useful life. This approach assumes that the asset loses a consistent amount of value each period until it reaches its salvage value, making it a straightforward and popular method in accounting for expense allocation.

Slope and Intercept in Linear Functions

In the context of a linear depreciation model, the slope represents the rate at which the asset's value decreases per unit of time, while the y-intercept indicates the initial value of the asset. These components are crucial for constructing and interpreting the linear equation that models the depreciation.

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