Q38. - 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.

Find the average rate of change of the number of Cassettes shipped from 1991 to 2000.

Step-by-Step Solution

Answer

The average rate of change of the number of Cassettes shipped from $1991$ to 2000 is $33.33.$

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, $(x_1,y_1)=(1991,400){\text{ and (x}}_2,y_2)=(2000,100)$

So,  $m=\frac{y_2-y_1}{x_2-x_1}$

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

Hence, the average rate of change of the number of Cassettes shipped from $1991$ to 2000 is $33.33.$