The table shows the height of a soccer ball that has been kicked from the ground over time. (for reference: h(t) = 144 – 16t2) time (seconds) height (feet) 0 0 0.5 16 1 24 1.25 25 1.5 24 2 16 2.5 0 which statement describes the rate of change of the height of the ball over time?

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.

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.

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.