Question

the table shows the number of grapes eaten over several minutes.
grapes eaten over time
time in minutes (x) | grapes eaten (y)
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 calculated as $\frac{\Delta y}{\Delta x}$, where $\Delta y$ is the change in the dependent variable (grapes eaten) and $\Delta x$ is the change in the independent variable (time in minutes).

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

Take two points from the table, e.g., $(x_1, y_1) = (1, 15)$ and $(x_2, y_2) = (2, 30)$. Then $\Delta y = 30 - 15 = 15$ and $\Delta x = 2 - 1 = 1$.

Step3: Compute rate of change

Using the formula $\frac{\Delta y}{\Delta x}$, we get $\frac{15}{1} = 15$. This means 15 grapes are eaten per minute.

Answer:

15 grapes eaten per minute