Chapter 3.1, Problem 45AYU

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 $\$2000$?

To determine

To calculate:

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 $\$2000$?

Answer to Problem 45AYU

Solution:

a. $V(x)=-1000x+3000$

b. The domain of the given function is $[0,3]$.

c. The graph is as shown below:

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

e. The computer will have a book value of $\$2000$ after one year.

Explanation of Solution

Given:

The company purchases a new computer for $\$3000$.

The depreciation is done for 3 years.

Calculation:

a.

Since the value of the computer is depreciated, the average rate of change of the computer is $-\$1000$.

Therefore, the linear function representing the book value of the computer is $V(x)=-1000x+3000$, where $V(x)$ is the value of the machine after each year and $V(0)$, which represents the original value of the computer is 3000.

b.

The value of $x$ in the given function can be any number between 0 and 3.

Therefore, the domain of the given function is $[0,3]$.

c.

The graph of the linear function is

d.

$V(2)=-1000(2)+3000$

$=1000$

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

e.

$2000=-1000(x)+3000$

$\Rightarrow x=\frac{3000-2000}{1000}=1$

The computer will have a book value of $\$2000$ after 1 year.