As part of a publicity stunt (an event designed to draw attention), a TV host drops a watermelon from the top of a tall building. The height of the watermelon f seconds after it is dropped is given by the function h(t) = 850 - 1612, where h is in feet. a. Find h(4). Explain what this value means in this situation. b. Find h(0). What does this value tell us about the situation? c. Is the watermelon still in the air 8 seconds after it is dropped? Explain how you know.

a) The value h(4) is 594 feet. In this situation, it represents the height of the watermelon 4 seconds after it was dropped from the top of the tall building. This means that after 4 seconds, the watermelon has fallen to a height of 594 feet.

b) The value h(0) is 850 feet. In this situation, it tells us that at the moment the watermelon is dropped from the top of the tall building (t = 0), its initial height is 850 feet above the ground.

c) The value h(8) is -174 feet. Since the height is negative, it means the watermelon has fallen below the ground level at t = 8. Therefore, the watermelon is no longer in the air 8 seconds after it was dropped.

Step-by-step explanation:

a. To find h(4), we substitute t = 4 into the function h(t):

h(4) = 850 - 16(4)^2

Simplifying the equation:

h(4) = 850 - 16(16)

h(4) = 850 - 256

h(4) = 594

The value h(4) is 594 feet. In this situation, it represents the height of the watermelon 4 seconds after it was dropped from the top of the tall building. This means that after 4 seconds, the watermelon has fallen to a height of 594 feet.

b. To find h(0), we substitute t = 0 into the function h(t):

h(0) = 850 - 16(0)^2

Simplifying the equation:

h(0) = 850 - 16(0)

h(0) = 850 - 0

h(0) = 850

The value h(0) is 850 feet. In this situation, it tells us that at the moment the watermelon is dropped from the top of the tall building (t = 0), its initial height is 850 feet above the ground.

c. To determine if the watermelon is still in the air 8 seconds after it is dropped, we need to check if its height is greater than 0 feet at t = 8. We can find h(8) by substituting t = 8 into the function h(t):

h(8) = 850 - 16(8)^2

Simplifying the equation:

h(8) = 850 - 16(64)

h(8) = 850 - 1024

h(8) = -174

The value h(8) is -174 feet. Since the height is negative, it means the watermelon has fallen below the ground level at t = 8. Therefore, the watermelon is no longer in the air 8 seconds after it was dropped.