To find the rate of change for the function on the table, we need to determine how the number of grapes eaten varies with time. This is typically calculated as the change in the number of grapes eaten divided by the change in time.
Here’s a detailed, step-by-step solution to find the rate of change:
1. Identify the values from the table:
- Time values (in minutes) are: 1, 2, 3, 4.
- Grapes eaten values are: [tex]\( y \)[/tex], 15, 30, 45, 60.
2. Calculate the changes in the number of grapes eaten and time:
- Change in grapes eaten from the first to the last value given is: [tex]\( 60 - 15 \)[/tex].
- Change in time from the first to the last value given is: [tex]\( 4 - 2 \)[/tex].
3. Compute the rate of change:
[tex]\[
\text{Rate of change} = \frac{\text{Change in grapes eaten}}{\text{Change in time}}
\][/tex]
[tex]\[
\text{Rate of change} = \frac{60 - 15}{4 - 2}
\][/tex]
[tex]\[
\text{Rate of change} = \frac{45}{2}
\][/tex]
[tex]\[
\text{Rate of change} = 15
\][/tex]
4. Interpret the result:
The rate of change is 15 grapes eaten per minute.
Therefore, the rate of change for the function on the table is 15 grapes eaten per minute.
