Question

the table shows the number of grapes eaten over several minutes.

grapes eaten over time
1	15
2	30
3	45
4	60

what is the rate of change for the function on the table?

• 15 grapes eaten per minute
• 15 minutes to eat each grape
• 60 grapes eaten per minute
• 60 minutes to eat each grape

Explanation:

Step1: Recall rate of change formula

The rate of change (slope) for a linear function is given by $\frac{\Delta y}{\Delta x}$, where $\Delta y$ is the change in $y$ (grapes eaten) and $\Delta x$ is the change in $x$ (time in minutes).

Step2: Calculate $\Delta y$ and $\Delta x$

Take two points, e.g., $(1, 15)$ and $(2, 30)$. $\Delta y = 30 - 15 = 15$, $\Delta x = 2 - 1 = 1$.

Step3: Compute rate of change

Rate of change $=\frac{\Delta y}{\Delta x}=\frac{15}{1}=15$. This means 15 grapes are eaten per minute.

Answer:

15 grapes eaten per minute