We want to know if the function given in the following table has a constant rate of change.
Time (s), x | Distance (m), y |
---|---|
4.82 | 40 |
6.49 | 60 |
8.13 | 80 |
9.69 | 100 |
We can check the rate of change algebraically by noting the change in x and change in y between each of the data points.
Changes between rows | change in xchange in y | Rate of change |
---|---|---|
1st→2nd | 1.6720 | ≈11.98 |
2nd→3rd | 1.6420 | ≈12.20 |
3rd→4th | 1.5620 | ≈12.82 |
As we can see, the rate of change is not constant. The runner had a higher average speed later in the race than in the middle.
We have been asked to find if the function given by the following table has a constant rate of change.
Time (s), x | Floor number, y |
---|---|
0 | 18 |
1.6 | 20 |
3.2 | 22 |
4.8 | 24 |
Let's find the change in x and change in y between each of the rows.
Changes between rows | change in xchange in y | Rate of change |
---|---|---|
1st→2nd | 1.62 | 1.25 |
2nd→3rd | 1.62 | 1.25 |
3rd→4th | 1.62 | 1.25 |
As we can see, the rate of change is constant. It tells us that the elevator's speed is 1.25 floors/second.