A student is completing a homework for each minute the student records the number of problems left to complete. The table shows data. What is the rate of change of this liner function? What does the rate of change represent in this situation?
Time (minutes) | 0 | 1 | 2 | 3 | 4 | 5 |
Problems Left | 29 | 25 | 21 | 17 | 13 | 9
To find the rate of change of this linear function, we can calculate the difference in the number of problems left between consecutive minutes.
First, let's find the difference in the number of problems left between each pair of consecutive minutes:
- From minute 0 to minute 1: 29 - 25 = 4
- From minute 1 to minute 2: 25 - 21 = 4
- From minute 2 to minute 3: 21 - 17 = 4
- From minute 3 to minute 4: 17 - 13 = 4
- From minute 4 to minute 5: 13 - 9 = 4
Since the difference is constant at 4, the rate of change of this linear function is 4.
In this situation, the rate of change represents the number of problems the student is able to complete in 1 minute. Since the rate of change is 4, it means that the student is able to complete 4 problems every minute.