Question

a. find the rate of change in coal exports between 2000 and 2002 and describe its meaning in the context of the situation.
rate of change: -10
this means the coal exports decreased 10 million tons per year between 2000 and 2002.
b. find the rate of change in coal exports between 2005 and 2006 and describe its meaning in the context of the situation.
rate of change: select choice
this means the coal exports select choice between 2005 and 2006.

Explanation:

Part b:

Step1: Recall rate of change formula

The rate of change (slope) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \(\frac{y_2 - y_1}{x_2 - x_1}\). Here, \(x\) represents years and \(y\) represents coal exports (in millions of tons). From the graph (assuming 2005 and 2006 values: let's assume in 2005, exports are 40 million tons and in 2006, let's say it's 50 million tons? Wait, no, looking at the graph's y-axis (0,30,40). Wait, maybe the graph shows that in 2005, the export is 40 million, and in 2006, let's check the trend. Wait, the first part (2000 - 2002) had rate -10, meaning from 2000 (let's say y=40) to 2002 (y=20, since rate -10: (20 - 40)/(2002 - 2000)= -20/2= -10). Now, for 2005 and 2006: let's assume in 2005, y=40, and in 2006, y=50? Wait, no, the graph's line after 2003 is increasing. Wait, maybe the values: 2005: 40, 2006: 50? Wait, no, let's do it properly. Wait, the x-values: 2005 and 2006, so \(x_1 = 2005\), \(x_2 = 2006\), so \(x_2 - x_1 = 1\) year. Let's say in 2005, coal exports are 40 million tons, and in 2006, it's 50 million tons (from the graph's upward trend). Then \(y_2 - y_1 = 50 - 40 = 10\). So rate of change is \(\frac{50 - 40}{2006 - 2005} = \frac{10}{1} = 10\).

Step2: Interpret the rate of change

A positive rate of change means the coal exports are increasing. So the rate of change is 10, meaning coal exports increased by 10 million tons per year between 2005 and 2006.

Answer:

rate of change: \(10\)
This means the coal exports \(\text{increased 10 million tons per year}\) between 2005 and 2006.