Chapter 4, Problem 10CT

To determine

The reasonable domain and range for the given situation is to be calculated.

Answer to Problem 10CT

Reasonable domain is,

  $0\le n\le 12.145$

Reasonable range is,

  $0\le C\left(n\right)\le 30$

Explanation of Solution

The cost of the each party favors = $\$2.47$

Maximum amount that can be spend on the party favors = $\$30$

To calculate the reasonable domain and range, the function is to form which can represent the situation.

From the given situation, it is observed that the cost is varying with the number of party favors. It means the cost is the dependent variable and number of part favors is independent variable.

Therefore the function or the situation becomes,

  $C\left(n\right)=2.47n$..........(1)

Where,

• $C\left(n\right)$ represents the cost of party favors.
• $n$ represents the number of party favors.

From the given data, the maximum numbers of party favors that can be bought are,

  $\begin{array}{l}{n}_{\max }=\frac{\$30}{\$2.47}\\ =12.145\end{array}$

The least number of party favors that can be bought is none. So, the least domain value is $0$ .

The most number of party favors that can be bought are $12.145$ . So, the greatest value of diamin is $12.145$ .

Therefore the domain becomes,

  $0\le n\le 12.145$

The range is calculated by plugging the least and most value of number of favors in the fucnction as follows:

  $\begin{array}{l}C\left(0\right)=2.47\times 0\\ =0\end{array}$

  $\begin{array}{l}C\left(12.145\right)=2.47\times 12\\ =30\end{array}$

Therefore the range becomes,

  $0\le C\left(n\right)\le 30$