the average price, in dollars, of a dozen large grade a eggs from 2005 to 2015 is shown in the graph…

Explanation:

Step1: Find data for 2006 - 2008

In 2006 (1 year since 2005), price is approximately $1.6$. In 2008 (3 years since 2005), price is approximately $1.8$.

Step2: Calculate average rate of change for 2006 - 2008

Average rate of change formula is $\frac{\Delta y}{\Delta x}=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $y_2 = 1.8$, $y_1=1.6$, $x_2 = 3$, $x_1 = 1$. So $\frac{1.8 - 1.6}{3 - 1}=\frac{0.2}{2}=0.1$.

Step3: Find data for 2005 - 2015

In 2005 (0 years since 2005), price is approximately $1.2$. In 2015 (10 years since 2005), price is approximately $2.4$.

Step4: Calculate average rate of change for 2005 - 2015

Using the formula $\frac{\Delta y}{\Delta x}=\frac{y_2 - y_1}{x_2 - x_1}$, with $y_2 = 2.4$, $y_1 = 1.2$, $x_2=10$, $x_1 = 0$. So $\frac{2.4 - 1.2}{10 - 0}=\frac{1.2}{10}=0.12$.

Answer:

The average rate of change of the price of a dozen eggs per year from 2006 to 2008 is $0.1$. The average rate of change of the price of a dozen eggs per year from 2005 to 2015 is $0.12$.