Chapter 3, Problem 20MCQ

(a)

To determine

Find the rate of change in approximate sales from 2003 to 2006.

Answer to Problem 20MCQ

30,000 sales/year

Explanation of Solution

Given :

The 2003 and 2006 sales figures for V Electronics are:

  

Formula Used:

Slope of a line passing through points $(x_1,y_1)\text{ and }(x_2,y_2)$ is $m=\frac{y_2-y_1}{x_2-x_1}$

Calculation :

Let the year be represented by x and the approximate sales be represented by y .

The rate of change in approximate sales with respect to the change in year :

Consider points (2003,240000) , (2006,330000) and find the slope

  $m=\frac{y_2-y_1}{x_2-x_1}=\frac{330000-240000}{2006-2003}=\frac{90000}{3}=30,000\text{ sales/year}$

Rate is positive, which indicates that sales are increasing each year .

(b)

To determine

Find the approximate sales for the year 2010 , if the rate remains same.

Answer to Problem 20MCQ

There are approximate sales of $450,000 in the year 2010.

Explanation of Solution

Formula Used:

Slope of a line passing through points $(x_1,y_1)\text{ and }(x_2,y_2)$ is $m=\frac{y_2-y_1}{x_2-x_1}$

Calculation :

From part (a) , the rate of approximate sales is 30,000 sales/year and

Approximate sales , $y_1$ = 330,000 in the year , $x_1$ = 2006.

Let approximate sales in the year , x = 2010 be y .

Since the rate of approximater sales remains same , we have:

  $\begin{array}{l}30,000=\frac{y-y_1}{x-x_1}\\ \Rightarrow \frac{y-330,000}{2010-2006}=30,000\\ \Rightarrow \frac{y-330,000}{4}=30,000\\ \Rightarrow y-330,000=120,\mathrm{000...............}[\text{multiply each side by 4]}\\ \Rightarrow y=120,000+330,\mathrm{000...............}[add\text{ 330,000 each side]}\\ \Rightarrow y=450,000\end{array}$

So, there are approximate sales of $450,000 in the year 2010.