Q39. - Algebra 2

Question

For Exercises 37-39, refer to the graph that shows the number of CDs and cassette tapes shipped by manufacturers to retailers in recent years.

39. Interpret the sign of your answer to Exercise 38.

Step-by-Step Solution

Answer

The cassette tapes shipped by manufacturers to retailers in years $1991$ to 2000 is very low.

Step 1- Given information

Table of the given data,

Step 2- Formula used

The slope formula (rate of change) m of a line is:

$m=\frac{y_2-y_1}{x_2-x_1}$

Where, m is slope of the line which is passes through the points $(x_1,y_1),(x_2,y_2)\text{ and }{x}_1\ne x_2.$

Step 3- To find the Rate of change

Here, $(x_1,y_1)=(1991,300){\text{ and (x}}_2,y_2)=(2000,900)$

So,  $m=\frac{y_2-y_1}{x_2-x_1}$

$\begin{array}{l}\Rightarrow m=\frac{100-400}{2000-1991}\\ \Rightarrow m=\frac{-300}{9}\\ \Rightarrow m=-33.33\end{array}$

It is the answer of the exercise 38.

Here, negative sign of answer shows that the cassettes are decreasing.

Hence, the cassette tapes shipped by manufacturers to retailers in years $1991$ to 2000 is very low.