Question

Question
Cupcake World makes the best cupcakes of all kinds. The graph shows the relationship of cupcakes baked and additional cups of sugar used to bake the cupcakes.

A line graph displays the relationship between the number of cupcakes baked and the additional cups of sugar used. The x-axis represents the additional cups of sugar, ranging from 0 to 50. The y-axis shows the number of cupcakes baked, ranging from 0 to 80. The line on the graph is steadily increasing, indicating a positive correlation: as the additional cups of sugar increase, so does the number of cupcakes baked. For example, 0 additional cups of sugar results in about 10 cupcakes baked, and 30 additional cups of sugar results in about 70 cupcakes baked.

What is the rate of change and what does it represent?

The rate of change is (blank), and represents
(blank)

Answer 1

To determine the rate of change from the information provided in the question, we need to analyze the relationship depicted in the line graph between the number of additional cups of sugar and the number of cupcakes baked.

The rate of change can be calculated as the change in the number of cupcakes baked divided by the change in the number of additional cups of sugar. Based on the provided data points:

1. When there are 0 additional cups of sugar, about 10 cupcakes are baked.
2. When there are 30 additional cups of sugar, about 70 cupcakes are baked.

Now, we calculate the change:
- Change in the number of cupcakes baked = 70 cupcakes - 10 cupcakes = 60 cupcakes.
- Change in additional cups of sugar = 30 cups - 0 cups = 30 cups.

Now, we can calculate the rate of change:

\[
\text{Rate of change} = \frac{\text{Change in cupcakes}}{\text{Change in sugar}} = \frac{60 \text{ cupcakes}}{30 \text{ cups}} = 2 \text{ cupcakes per cup of sugar}
\]

Thus, we can fill in the blanks as follows:

The rate of change is **2 cupcakes per cup of sugar**, and represents **the number of cupcakes baked for each additional cup of sugar used**.