Beginning Algebra With Applications, Chapter 5, 5.5, Section 5.5, Problem 62

Depreciation is the declining value of an asset. For instance, a company purchases a truck for $\$ 20,000$. The truck is an asset worth $\$ 20,000$. In 5 years, however, the value of the truck will have declined, and it may be worth only $\$ 4000$. An equation that represents this decline is $V = 20,000 - 3200x$, where $V$ is the value, in dollars, of the truck after $x$ years.

a. Write the equation in functional notation.

The equation $V = 20,000 - 3200x$ can be written in functional notation as $f(x) = 20,000 - 3200x$

b. Use the coordinate axes to graph the equation for values of $x$ between 0 and 5.

Using the equation in part a. Substitute values of $x = \{ 0,1,2,3,4,5 \}$


$\begin{equation} \begin{aligned} f(0) =& 20,000 - 3,200(0) = 20,000 \\ f(1) =& 20,000 - 3,200(1) = 16,800 \\ f(2) =& 20,000 - 3,200(2) = 13,600 \\ f(3) =& 20,000 - 3,200(3) = 10,400 \\ f(4) =& 20,000 - 3,200(4) = 7,200 \\ f(5) =& 20,000 - 3,200(5) = 4,000 \end{aligned} \end{equation}$



The ordered pairs are $(0,20000), (1,16800), (2,13600), (3,10400), (4,7200)$ and $(5,4000)$







c. The point $(4,7200)$ is on the graph. Write a sentence that explains the meaning of this ordered pair.

The point $(4,7200)$ means that in four years the value of the truck will be worth $\$ 7,200$.