Chapter 2.1, Problem 94AYU

a)

To determine

To identify: the dependent and the independent variables for the given function.

Answer to Problem 94AYU

The dependent and the independent variables for the given function are N and r respectively.

Explanation of Solution

Given information:

A housing unit function is given as

  $N\left(r\right)=-1.44r^2+14.52r-14.96$

Here $N$ is number of housing units in millions and $r$ is number of rooms such that $2\le r\le 9$ .

Concept used:

Consider two sets A and B . If each element $x$ in the set A has exactly one element $y$ in the set B, the relation between them is known as a function. The ordered pair is $\left(x,y\right)$ .

The values of first coordinate $x$ is known as input values and the values of second coordinate $y$ is known as output values of a function.

For each random value of $x$ , the variable $y$ will give a different value.

So, value of $y$ is dependent on each value of $x$ .

Calculation:

Consider the given function.

  $N\left(r\right)=-1.44r^2+14.52r-14.96$

Here, for every input of roomr , housing unit numberN has a specific output.

Therefore, for the equation $N\left(r\right)=-1.44r^2+14.52r-14.96$ , number of rooms $r$ is independent variable and number of housing units N is dependent variable.

b)

To determine

To find: the value of $N\left(3\right)$ and interpret the result.

Answer to Problem 94AYU

  $N\left(3\right)=15.64$ million.

  $N\left(3\right)=15.64$ million means in 2005 there was 15.64 million housing units that have 3 rooms.

Explanation of Solution

Given information:

A housing unit function is given as

  $N\left(r\right)=-1.44r^2+14.52r-14.96$

Here $N$ is number of housing units in millions and $r$ is number of rooms such that $2\le r\le 9$ .

Calculation:

Consider the given function.

  $N\left(r\right)=-1.44r^2+14.52r-14.96$

For evaluating $N\left(3\right)$ , substitute 3 for r in above equation.

  $\begin{array}{c}N\left(3\right)=-1.44{\left(3\right)}^2+14.52\left(3\right)-14.96\\ =15.64\end{array}$

Here $N$ is number of housing units in millions and $r$ is number of rooms such that $2\le r\le 9$ .

  $N\left(3\right)=15.64$ million means in 2005 there was 15.64 million housing units that have 3 rooms.