Question

The graph below shows the increase in the population of individuals over a certain number of years.

1). Calculate the average rate of change using the interval [0, 10].


2). Interpret the average rate of change for this problem.

Answer 1

25 people per year

Explanation:

The average rate of change, or slope of a straight line, between two points is:

`m = (\Delta y)/(\Delta x)`

where
`\Delta y` is the vertical change between the points, and
`\Delta x` is the horizontal change.

We can identify the following values from the graph:

• 
  `\Delta y = 650 - 400 = 250 \text{ people}`
• 
  `\Delta x = 10\text{ years}`

Now, we can use these to solve for the average rate of change:

`m = \frac{250 \text{ people}}{10\text{ years}}`

`m=\frac{25\text{ people}}{1\text{ year}}`

`\boxed{m = 25 \text{ people per year}}`