The table provided shows the population of a town (in thousands) between the years 2000 and 2008. We are tasked with calculating the average rate of change in population between:

1. 2002 and 2004
2. 2002 and 2006

(a) Average rate of change between 2002 and 2004:

To calculate the average rate of change between two years, we use the formula:

$\text{Average rate of change} = \frac{\text{Population at later year} - \text{Population at earlier year}}{\text{Later year} - \text{Earlier year}}$

For the years 2002 and 2004:

• Population in 2002: 82,000
• Population in 2004: 77,000

$\text{Rate of change} = \frac{77 - 82}{2004 - 2002} = \frac{-5}{2} = -2.5 \text{ thousand people per year}$

So, the average rate of change between 2002 and 2004 is -2.5 thousand people per year.

(b) Average rate of change between 2002 and 2006:

For the years 2002 and 2006:

• Population in 2002: 82,000
• Population in 2006: 78,000

$\text{Rate of change} = \frac{78 - 82}{2006 - 2002} = \frac{-4}{4} = -1 \text{ thousand people per year}$

So, the average rate of change between 2002 and 2006 is -1 thousand people per year.

Would you like more details or have any further questions?

Here are 5 follow-up questions to expand on the topic:

1. How does the average rate of change between other consecutive years compare to these?
2. What is the total population change between 2000 and 2008?
3. What does a negative rate of change indicate in terms of population dynamics?
4. Can we predict population trends beyond 2008 based on the given data?
5. How would the rate of change differ if we calculated it for shorter or longer intervals?

Tip: The average rate of change is essentially the slope of the line between two points on a graph of the data!