91Ó°ÊÓ

A company has just purchased a new computer for $3000. The company choose depreciation of the computer using the straight-line method over 3 years.

Find a linear model that expresses the book value V of the computer as a function of its agex.

The original value of computer as $V\left(0\right)$is $3000. This y-intercept of the linear function.

The depreciation per year is $\frac{3000}{3}=1000$. So, slope is -1000.

The linear function that represents the book value V of the computer as a function of its agexis$V\left(x\right)=-1000x+3000$.

Find the implied domain of the function.

The depreciation period of the computer is 3 yrs.

so x varies from0 to 3.

The implied domain of the function is$\left\{x|0≤x≤3\right\}$.

the graph of the linear function on domain $\left[0,3\right]$is as follows.

Find the book value of the computer after 2 years.

Here, $x=2$

Substitute $x=2$in role="math" localid="1646849549182" $V\left(x\right)=-1000x+3000$.

$$\begin{gathered} V\left(x\right)=-1000x+3000 \\ =-1000\left(2\right)+3000 \\ =1000 \end{gathered}$$

The book value of the computer after 2 years is $1000.

Find by when a book value of the computer will be $2000.

we have $V\left(x\right)=2000$Find x.

$$\begin{gathered} V\left(x\right)=-1000x+3000 \\ 2000=-1000x+3000 \\ -1000=-1000x \\ 1=x \end{gathered}$$

After 1 year a book value of the computer will be $2000 .