Question
A student is completing a homework assignment. Each minute the student records the number of problems left to complete. The table shows the data. What is the rate of change of this linear function? What does the rate of change represent in this situation?
Homework Assignment
Time (minutes)
0
1
2
3
4
5
Problems Left
14
12
10
8
6
4
Question content area bottom
Part 1
What is the rate of change of this linear function?
The rate of change is
enter your response here.
Homework Assignment
Time (minutes)
0
1
2
3
4
5
Problems Left
14
12
10
8
6
4
Question content area bottom
Part 1
What is the rate of change of this linear function?
The rate of change is
enter your response here.
Answers
GPT-4o mini
To calculate the rate of change of the linear function represented by the data in the table, we can use the formula for the rate of change, which is:
\[
\text{Rate of Change} = \frac{\text{Change in Problems Left}}{\text{Change in Time}}
\]
From the table:
- At time \(0\) minutes, there are \(14\) problems left.
- At time \(5\) minutes, there are \(4\) problems left.
To find the total change in problems left:
\[
\text{Change in Problems Left} = 4 - 14 = -10
\]
And the total change in time:
\[
\text{Change in Time} = 5 - 0 = 5
\]
Now, substituting these values into the formula gives us:
\[
\text{Rate of Change} = \frac{-10}{5} = -2
\]
### Part 1 Answer:
The rate of change is **-2**.
### Interpretation:
The rate of change represents the number of problems the student completes per minute. In this case, a rate of **-2** means that the student completes **2 problems each minute**.
\[
\text{Rate of Change} = \frac{\text{Change in Problems Left}}{\text{Change in Time}}
\]
From the table:
- At time \(0\) minutes, there are \(14\) problems left.
- At time \(5\) minutes, there are \(4\) problems left.
To find the total change in problems left:
\[
\text{Change in Problems Left} = 4 - 14 = -10
\]
And the total change in time:
\[
\text{Change in Time} = 5 - 0 = 5
\]
Now, substituting these values into the formula gives us:
\[
\text{Rate of Change} = \frac{-10}{5} = -2
\]
### Part 1 Answer:
The rate of change is **-2**.
### Interpretation:
The rate of change represents the number of problems the student completes per minute. In this case, a rate of **-2** means that the student completes **2 problems each minute**.