Question

Find the average rate of change in cigarette consumption for the years shown during which consumption was decreasing. Round to one decimal place, ifnecessary

Answer 1

-75 billion cigarettes per year

Step-by-step explanation

We want to find the average rate of change in cigarette consumption for the years when the consumption is decreasing.

To do this, we have to find the start point of the decrease and the end point of the decrease. Then, we use the formula for slope to find the cigarette consumption per year.

The reason for using just the start point and end point is that the question askes for average.

The start point of the decrease is (1970, 600) and the end point is (2010, 300).

So, the slope is:

`\begin{gathered} \text{slope = }\frac{300\text{ - 600}}{2010\text{ - 1970}}\text{ = }(-300)/(40) \\ \text{slope = -75 billion cigarettes per year} \end{gathered}`

This means that the averate rate of change of cigarettes consumption per year when the consumption was decreasing is -75 billion cigarettes per year.

Note: The negative sign there confirms for us that the consumption is decreasing.