Chapter 1.4, Problem 31E

a.

To determine

To find: value of average annual rate of increase.

Answer to Problem 31E

$6111 billion per year

Explanation of Solution

Given information:

Retail sale in 1995 = $70583 billion

Retail sale in 1997 = $82805 billion

Assume a linear relation to solve the question.

Calculation:

Evaluate the increase in duration for the given sales as follows:

  $\begin{array}{c}\text{Increase in year}=1997-19995\\ =2\end{array}$

Evaluate the increase in sales over 2 years as follows:

  $\begin{array}{c}\text{Increase in sales over 2 years}=\$82805\text{ billion}-\$70583\text{ billion}\\ =\$12222\text{ billion}\end{array}$

Thus, the increase in sales over 2 years is $\$12222\text{ billion}$ .

As the increase is linear, then the sale increase will be same for each year. The increase of sales for 1 year will be evaluated as follows:

  $\begin{array}{c}\text{Increase in sales over 1 years}=\frac{\$12222\text{ billion}}{2}\\ =\$6111\text{ billion}\end{array}$

Thus, the average annual rate of increase in sales is $\$6111\text{ billion per year}$ .

b.

To determine

To explain: the relationship between rate and graph of line.

Answer to Problem 31E

The value of $\text{'}s\text{'}$ changes according to $\text{'}t\text{'}$ times the slope i.e. $\text{'}r\text{'}$ .

Explanation of Solution

Given information:

Retail sale in 1995 = $70583 billion

Retail sale in 1997 = $82805 billion

Average annual rate of increase of sales is $6111 billion per year.

Calculation:

Let $s,r$ and $t$ be as follows:

  $\begin{array}{l}s=\text{sales}\\ r=\text{rate of increase}\\ t=\text{ time}\end{array}$

The graph of line will be as follows:

  $s=rt$

Since the value of r is $6111 billion per year. Thus, r is constant and it denotes the slope.

The variables are s and t . The variable s is dependent on t . Thus, we can say that $\text{'}s\text{'}$ according to changes in $\text{'}t\text{'}$ times the slope i.e. $\text{'}r\text{'}$ .