Question

The table shows the height of a soccer ball that has been kicked from the ground over time. (For reference: h(t) = −16t2 + 40t) 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? 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. 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. 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. 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 1

- Between 0 and 0.5 second the ball rises 16 feet, but between 0.5 and 1 second it rises only 8 more feet

- 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

- The height of the ball above ground gets larger until 1.25 seconds and then gets smaller after that time.

Explanation:

Let's rewrite the table:

Time (seconds) Height (feet)

0 0

0.5 16

1 24

1.25 25

1.5 24

2 16

2.5 0

By simply looking at the table, we can see that the following statements are all correct:

- Between 0 and 0.5 second the ball rises 16 feet, but between 0.5 and 1 second it rises only 8 more feet

- 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

- The height of the ball above ground gets larger until 1.25 seconds and then gets smaller after that time.