To find the constant rate of change in the table, let's calculate the rate of change between the quantities (Cost and Dozens Bought) step by step:

Table:

Formula for Rate of Change:

$\text{Rate of Change} = \frac{\Delta y}{\Delta x} = \frac{\text{Change in Cost}}{\text{Change in Dozens Bought}}$

Step 1: Calculate rate of change for each interval

1. From 2 to 4 dozen: $\text{Rate} = \frac{6.50 - 3.25}{4 - 2} = \frac{3.25}{2} = 1.625 \, \text{(dollars per dozen)}.$

2. From 4 to 6 dozen: $\text{Rate} = \frac{9.75 - 6.50}{6 - 4} = \frac{3.25}{2} = 1.625 \, \text{(dollars per dozen)}.$

3. From 6 to 8 dozen: $\text{Rate} = \frac{13.00 - 9.75}{8 - 6} = \frac{3.25}{2} = 1.625 \, \text{(dollars per dozen)}.$

Step 2: Confirm constant rate of change

The rate of change is the same for each interval, so the constant rate of change is 1.625 dollars per dozen.

Final Answer:

The constant rate of change is: $1.625 \, \text{dollars per dozen}.$

Would you like further explanation, or do you have any additional questions?

Related Questions:

1. What is the slope of the line representing the relationship in this table?
2. How much would 10 dozens of donuts cost at this rate?
3. Can you write a linear equation that models this relationship?
4. Is this relationship proportional, and why?
5. How does the constant rate of change help predict costs for any number of dozens?

Tip:

The constant rate of change is also the slope in a linear relationship. Always verify it remains consistent across all intervals!