Let’s solve this step-by-step.

(a) Writing the linear function for depreciation:

The straight-line depreciation method reduces the value of an asset by a fixed amount each year. For this problem:

• The initial value of the computer is $\$2400$.
• The depreciation period is 3 years.
• At the end of 3 years, the computer’s value will be $\$0$.

The depreciation per year is:

$\text{Depreciation rate} = \frac{\$2400 - 0}{3} = \$800 \, \text{per year}$

The book value $V$ of the computer decreases by $800 each year, so the linear function representing the book value $V(x)$ as a function of its age $x$ (in years) is:

$V(x) = 2400 - 800x$

Where:

• $V(x)$ is the book value after $x$ years.
• $x$ is the age of the computer in years.

(b) Domain of the function:

The domain of the function corresponds to the time during which the depreciation takes place. The company depreciates the computer over 3 years, so the age $x$ must be between 0 and 3 years (inclusive). Therefore, the domain is:

$\text{Domain: } [0, 3]$

(c) Graphing the linear function:

The function $V(x) = 2400 - 800x$ is a straight line with:

• Y-intercept $V(0) = 2400$, which represents the initial value.
• X-intercept at $x = 3$, where the book value drops to $0$.

Let me sketch the graph for you.

(d) Book value after 2 years:

To find the book value after 2 years, substitute $x = 2$ into the linear function:

$V(2) = 2400 - 800(2) = 2400 - 1600 = 800$

So, the book value after 2 years is $800.

(e) When will the computer have a book value of $1600?

We can solve for $x$ by setting $V(x) = 1600$:

$1600 = 2400 - 800x$

Now solve for $x$:

$1600 - 2400 = -800x$ $-800 = -800x$ $x = 1$

So, the computer will have a book value of $1600 after 1 year.

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Would you like the graph or further details on any step?

Here are 5 related questions:

1. How does straight-line depreciation compare to other methods like declining balance?
2. What would the function look like if the depreciation were over 5 years instead of 3?
3. How would the function change if the initial value of the computer were $3000?
4. What happens to the graph if the depreciation rate is not constant?
5. How does the domain affect the graph of the depreciation function?

Tip: Always ensure the domain reflects the useful life of the asset in straight-line depreciation problems.