Chapter 1.7, Problem 45PPS

a.

To determine

To predict: The relationship between class size and class average from the given graph.

Answer to Problem 45PPS

As the class size increases class average decreases.

Explanation of Solution

Given Information: Function is $f(z)=-\frac{5}{8}z+87$ .

Graph:

  Interpretation:

As is evident from the graph, line is making a negative slope, this implies that as the class size increases class average decreases.

b.

To determine

To find: The class size that corresponds to a class average of $72$ .

Answer to Problem 45PPS

The class size is $24$ .

Explanation of Solution

Given Information: Function is $f(z)=-\frac{5}{8}z+87$ .

Calculation:

  $f(x)=72(Given)$

  $\begin{array}{l}\Rightarrow 72=-\frac{5}{8}z+87\\ -\frac{5}{8}z=-15\\ z=\frac{15\times 8}{5}\\ z=24\end{array}$

Thus, the class size is $24$ .

c

To determine

To find: The domain and range of the given function.

Answer to Problem 45PPS

Domain is a set of positive integers and range is $\{-\frac{5}{8}z+87:z\in Z^{+}\}$ .

Explanation of Solution

Given Information: Function is $f(z)=-\frac{5}{8}z+87$ .

Calculation:

Since the number of students can be integers, so

Domain: Set of positive integers.

Range: $\{-\frac{5}{8}z+87:z\in Z^{+}\}$

Thus, domain is a set of positive integers, i.e., $Z^{+}$ and range is $\{-\frac{5}{8}z+87:z\in Z^{+}\}$ .