Chapter 1 - Functions and Their Graphs - Section 1.6 Mathematical Models: Building Functions - 1.6 Assess Your Understanding - Page 104: 14

a) $P(x)=x$ b) $A(x)=\dfrac{x^2}{16}$

(a) The length of the side of the square is $r=\dfrac{x}{4}$ So, the perimeter will be the length of the wire: $P(x)=4*side=4*\frac{x}{4}=x$ b) The length of the side of the square is $r=\dfrac{x}{4}$ So, the area is: $A(x)=side^2=(\dfrac{x}{4})^2=\dfrac{x^2}{16}$