The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds: A linear model with ordered pairs at 0, 60 and 2, 80 and 3, 80 and 4, 20 and 6, 0 and 7, 0 and 8, 0. The x axis is labeled Time in seconds, and the y axis is labeled Height in feet.

Part A: During what interval(s) of the domain is the water balloon's height increasing? (2 points)

Part B: During what interval(s) of the domain is the water balloon's height staying the same? (2 points)

Part C: During what interval(s) of the domain is the water balloon's height decreasing the fastest? Use complete sentences to support your answer. (3 points)

Part D: Use the constraints of the real-world situation to predict the height of the water balloon at 10 seconds. Use complete sentences to support your answer. (3 points)

See below.

Step-by-step explanation:

So we can picture a graph with the following coordinates:

So the graph should begin at y=60, go up a little, stay there a little, and then start falling downwards.

Part A:

The intervals of the domain where the balloon's height is increasing is right after the release (0,60) until the second second at (2,80). We can see that between these two seconds, the height increased by 20 feet. After that point, the balloon starts falling down and won't rise again. At exactly the second second, however, the balloon is staying still so we won't include the second. Thus, we will use parentheses. Therefore, the interval is:

Part B:

As we can see, the balloon stays the same from the second second up to the third second. At those exact seconds, they are also within the same height, so we include them. Thus:

Part C:

So, we have two intervals where the balloon's height is decreasing. From (3,80) to (4,20) and also from (4,20) to (6,0). Using the slope formula, we can see that the balloon drops at a rate of 60 feet per second. The second interval only drops at a rate of 10 feet per second. We don't know the height of the balloon at x equals 5 seconds, but that doesn't matter since it can be greater than 60 feet per second. Thus, the interval during which the balloon's height is decreasing the fastest is:

Part D:

After and during the sixth, seventh, and eighth seconds, the balloon's height is 0, meaning it's completely on the ground. Without any force such as wind, the balloon would stay there. Therefore, at 10 seconds, the height of the water balloon should still be 0, on the ground.

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step-by-step explanation: