Answer:
The answer is below
Step-by-step explanation:
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, 75 and 4, 75 and 6, 40 and 8, 20 and 10, 0 and 12, 0 and 14, 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 16 seconds.
Answer:
Part A: During what interval(s) of the domain is the water balloon's height increasing?
Between 0 and 2 seconds, the height of the balloon increases from 60 feet to 75 feet
Part B: During what interval(s) of the domain is the water balloon's height staying the same?
Between 2 and 4 seconds, the height remains the same at 75 feet. Also from 10 seconds the height of the balloon is at 0 feet
Part C: During what interval(s) of the domain is the water balloon's height decreasing the fastest?
Between 4 and 6 seconds, the height of the balloon decreases from 75 feet to 40 feet (i.e. -17.5 ft/s)
Between 6 and 8 seconds, the height of the balloon decreases from 40 feet to 20 feet (i.e. -10 ft/s)
Between 8 and 10 seconds, the height of the balloon decreases from 20 feet to 0 feet (i.e. -10 ft/s)
Hence it decreases fastest from 4 to 6 seconds
Part D: Use the constraints of the real-world situation to predict the height of the water balloon at 16 seconds
From 10 seconds, the balloon is at the ground, so it remains at the ground (0 feet) even at 16 seconds
