Q. 94 - Precalculus Enhanced with Graphing Utilities

Question

Number of Rooms The function $N\left(r\right)=-1.44r^2+14.52r-14.96$

represents the number $N$ of housing units (in millions) that have $r$rooms, where $r$ is an integer and $2\le r\le 9$.

(a) Identify the dependent and independent variables.

(b) Evaluate N(3). Provide a verbal explanation of the meaning of $N\left(3\right)$.

Step-by-Step Solution

Answer

(a) The dependent variable is $N$ and independent variable is $r$.

(b) The value of $N\left(3\right)=15.64$, there are $15.64$ housing units (in millions) that have $3$ rooms.

Step 1. Given Information

The function$N\left(r\right)=-1.44r^2+14.52r-14.96$ represents the number $N$ of housing units (in millions) that have $r$ rooms, where $r$ is an integer and $2\le r\le 9$.

(a) Identify the dependent and independent variables.

(b) Evaluate $N\left(3\right)$. Provide a verbal explanation of the meaning of $N\left(3\right)$.

Part (a) Step 1. We have to identify the dependent and independent variables. The given function is N ( r ) = - 1 . 44 r 2 + 14 . 52 r - 14 . 96

As we know, the dependent variable is characterized as the variable whose quality depends on the estimation of another variable in its condition. 

In this given function $N$ depends on the estimation of another variable in its condition.

So the dependent variable is $N$.

Part (a) Step 2. As we know, an independent variable describes a variable whose values are independent of changes.

In this given function variable $r$ are independent of changes.

So the independent variable is $r$.

Part (b) Step 1. Evaluating the value of N ( 3 ) . Putting N = 3 on the given function.

$$\begin{gathered} N\left(3\right)=-1.44{\left(3\right)}^2+14.52\times 3-14.96 \\ N\left(3\right)=-1.44\times 9+14.52\times 3-14.96 \\ N\left(3\right)=-12.96+43.56-14.96 \\ N\left(3\right)=15.64 \end{gathered}$$

Part (b) Step 2. A verbal explanation of the meaning of N ( 3 ) .

The meaning of $N\left(3\right)$ is ", there are $15.64$ housing units (in millions) that have 3 rooms.