Question

Using the graph, find the rate of change of a country's defense outlays.

Answer 1

To answer this question, we have:

1. There is a linear function. In the x-axis, we have years (x variable). IN the y-axis, we have the spending in the country's defense outlays.

2. The rate of change here is given by the slope of the line, and it is given by the following formula:

`m=(y_2-y_1)/(x_2-x_1)`

3. We can identify two points in the graph to find this slope. Remember, since this is a linear function, the value of the slope remains the same for the function.

4. We have years on the x-axis. However, to find the slope, we need to find years after 1991 to find this slope.

Therefore, the points could be ( 1, 290), (3, 260). We can see that after one year from 1991 (1992) we have 290 billion, and, also, for the year 3 after 1991 (1994), we have 260 billion.

5. Finally, the rate of change of a country's defense outlays is:

• (1, 290) ---> x1 = 1, y1 = 290

,

• (3, 260) ---> x2 = 3, y2 = 260

`\begin{gathered} m=(260-290)/(3-1) \\ m=(-30)/(2) \\ m=-15 \end{gathered}`

Therefore, Defense spending is decreasing by 15 billion (in current dollars) per year.