27. Height decreased at 0.375 units/sec from 3s to 6s.
28. Height increased at 0.427 units/sec from 7s to 10s.
27. To find the rate of change over the interval 3 ≤ t ≤ 6, we can use the following formula:
rate of change = (change in y) / (change in x)
where y is the height and x is the time
We can see from the graph that the height changes from 4 to 12 feet over the interval 27.3 ≤ t ≤ 6. Therefore, the rate of change is:
rate of change = (12 - 4) / (6 - 27.3) = 8 / -21.3 = -0.375 units per second
Since the rate of change is negative, we know that the height is decreasing.
28. To find the rate of change over the interval 7 ≤ t ≤ 10, we can use the same formula:
rate of change = (change in y) / (change in x)
where y is the height and x is the time.
We can see from the graph that the height changes from 12 to 4 feet over the interval 28.7 ≤ t ≤ 10. Therefore, the rate of change is:
rate of change = (4 - 12) / (10 - 28.7) = -8 / -18.7 = 0.427 units per second
Since the rate of change is positive, we know that the height is increasing.