To model this situation with a linear function, we use the formula for a linear function:

$f(x) = mx + b$

Where:

• $f(x)$ is the average amount of chicken consumed after $x$ years,
• $m$ is the rate of change (slope),
• $b$ is the initial value (y-intercept),
• $x$ is the number of years after 2006.

Given:

• In 2006, the average adult ate 55 pounds of chicken, so $b = 55$.
• The amount increases by 0.8 pounds per year, so the slope $m = 0.8$.

Thus, the linear function is:

$f(x) = 0.8x + 55$

Here, $x$ represents the number of years after 2006. For example, in 2007 ($x = 1$), the model predicts:

$f(1) = 0.8(1) + 55 = 55.8 \, \text{pounds}$

This linear function applies until 2011 ($x = 5$).

Do you want more details or have any questions?

Here are some additional questions related to this scenario:

1. What will the average consumption be in 2011 using this model?
2. How much chicken would an adult have eaten by 2010 according to the function?
3. If the trend continued beyond 2011, what would the consumption be in 2012?
4. How would the function change if the rate of increase was 1 pound per year instead of 0.8 pounds?
5. How can you interpret the slope in terms of the real-world situation?

Tip: In a linear function, the slope $m$ represents the rate of change, while the y-intercept $b$ is the initial value at $x = 0$.