This question comes with these answer choices:
A) The rate of change is not constant and decreases over the entire time. Between 0 and 0.5 second the ball rises 16 feet, but between 0.5 and 1 second it rises only 8 more feet.
B) The rate of change is not constant and increases over the entire time. Between 1.5 and 2 seconds the ball falls 8 feet, but between 2 and 12.5 seconds it falls 16 more feet.
C) The rate of change is not constant and decreases then increases over time. The ball rises by 16 in the first half second, but only 8 feet over the next one. After it reaches 25 feet in the air, the ball drops.
D) The rate of change is not constant and increases then decreases over time. The height of the ball above ground gets larger until 1.25 seconds and then gets smaller after that time.
Answer: option D). The rate of change is not constant and increases then decreases over time. The height of the ball above ground gets larger until 1.25 seconds and then gets smaller after that time.
Step-by-step explanation:
1) The rate of change of the function is defined and calculated as:
r = [change in height ] / [ change in time]
2) Table
Here I show the calculations for the rate of change (r) for each interval given, using the same of the table.
The conclusion with the answer follows fron it.
Time Height change in height change in time r
seconds feet feet seconds feet / seconds
0 0
0.5 16 16 - 0 = 16 0.5 16 / 0.5 = 32
1 24 24 - 16 = 8 0.5 8 / 0.5 = 16
1.25 25 25 - 24 = 1 0.25 1 / 0.25 = 4
1.5 24 24 - 25 = - 1 0.25 - 1 / 0.25 = - 4
2 16 16 - 24 = - 8 0.5 - 8 / 0.5 = - 16
2.5 0 0 - 16 = - 16 0.5 - 16 / 0.5 = - 32
3) Conclusion
The data in the third and fiths column show that: The rate of change is not constant and increases then decreases over time. The height of the ball above ground gets larger until 1.25 seconds and then gets smaller after that time.