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A company has just purchased a new machine for its manufacturing facility for $120,000. It chooses to depreciate the machine using the straight-line method over 10 years.

Find a linear model that expresses the book value V of the machine as a function of its age x.

The original value of Machine as $V\left(0\right)$ is $120000. This y-intercept of the linear function.

The depreciation period is 10 years.

The depreciation per year is $\frac{120000}{10}=12000$So, slope is -12000.

The linear function that represents the book value V of the machine as a function of its age x is$V\left(x\right)=-12000x+120000$

Find the implied domain of the function.

The depreciation period of machine choose by company is 10 years.
so, x varies from 0 to 10.

The implied domain of the function is$\left\{x|0≤x≤10\right\}$.

The graph of the linear function$v\left(x\right)=-12000x+120000$on domain $\left[0,3\right]$is as follows.

Find the book value of the machine after 4 years.

We have $x=4$, find $V\left(x\right)$.

$$\begin{gathered} V\left(x\right)=-12000x+120000 \\ =12000\left(4\right)+120000 \\ =72000 \end{gathered}$$

The book value of the machine after 4 years is $72000.

Find by when a book value of the machine will be of $72,000 .

We have $V\left(x\right)=72000$Find x

$$\begin{gathered} V\left(x\right)=-12000x+120000 \\ 72000=-12000x+120000 \\ -48000=-12000x \\ 4=x \end{gathered}$$

After 4 year a book value of the computer will be $ 72000.