Beginning Algebra With Applications, Chapter 5, 5.5, Section 5.5, Problem 64

An architect charges a fee of $\$ 500$ plus $2.65$ per square foot to design a house. The equation that represents the architect's fee is given by $F = 2.65s + 500$, where $F$ is the fee, in dollars, and $s$ is the number of square feet in the house.

a. Write the equation in functional notation.

The equation $F = 2.65s + 500$ can be written in functional notation as $f(s) = 2.65s + 500$, where $f(x)$ is the fee, in dollars and $s$ is the number of square feet in the house.

b. Use the coordinate axes to graph the equation for values of $s$ between 0 and 5000.

Using the equation in part a. Substitute values of $s = \{ 0,500,1000,1500,2000,2500,3000,3500,4000,4500,5000 \}$


$\begin{equation} \begin{aligned} f(0) =& 2.65(0) + 500 = 500 \\ f(500) =& 2.65(500) + 500 = 1825 \\ f(1000) =& 2.65(1000) + 500 = 3150 \\ f(1500) =& 2.65(1500) + 500 = 4475 \\ f(2000) =& 2.65(2000) + 500 = 5800 \\ f(2500) =& 2.65(2500) + 500 = 7125 \\ f(3000) =& 2.65(3000) + 500 = 8450 \\ f(3500) =& 2.65(3500) + 500 = 9775 \\ f(4000) =& 2.65(4000) + 500 = 11100 \\ f(4500) =& 2.65(4500) + 500 = 12425 \\ f(5000) =& 2.65(5000) + 500 = 13750 \\ \end{aligned} \end{equation}$


The ordered pairs are $(0,500), (500,1825), (1000,3150), (1500,4475), (2000,5800), (2500,7125), (3000,8450), (3500,9775), (4000,11100), (4500,12425)$ and $(5000,13750)$







c. The point $(3500,9775)$ is on the graph. Write a sentence that explains the meaning of this ordered pair.

The ordered pair $(3500,9775)$ means that if the house is $3500$ ft $^2$, the architect charges a fee of $\$ 9,775$.