Chapter 2.FOM, Problem 1P

To determine

To find:

A function that models area in terms of width.

Answer to Problem 1P

Solution:

The area of the building modeled by the function $A(w)=3w^2,w>0$.

Explanation of Solution

The model we want is a function that gives the area of the rectangular building.

For the rectangular building,

$Area=Length\times Width$

There are two varying quantities: Length and Width.

But the function we want depends on the width w.

We must express the length in terms of its width w. Because the length of the building is three times as long as it is wide. If we let length be l, then we have,

$l=3w$

The model is the function A that gives the area of the rectangular building for any width w.

$\begin{array}{l}Area=Length\times Width\\ A(w)=3w\times w\\ A(w)=3w^2,w>0\end{array}$

Thus, the area of the building modeled by the function $A(w)=3w^2,w>0$.

Final statement:

The area of the building modeled by the function $A(w)=3w^2,w>0$.