Question

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.

a: During what interval(s) of the domain is the water balloon's height increasing?
b: During what interval(s) of the domain is the water balloon's height staying the same?
c: During what interval(s) of the domain is the water balloon's height decreasing the fastest? Use complete sentences to support your answer.
d: Use the constraints of the real-world situation to predict the height of the water balloon at 16 seconds. Use complete sentences to support your answer.

Answer 1

The water balloon's height increases from 0 to 2 seconds, stays the same from 2 to 4 seconds, and decreases the fastest between 4 and 6 seconds. At 16 seconds, the height of the water balloon is predicted to remain at 0 feet due to real-world constraints.

Step-by-step explanation:

To understand the behavior of the water balloon's height over time based on the given linear model, we will look at the intervals of time where the height changes. The student asked:

1. Height increasing: The water balloon's height is increasing from the start until it reaches its maximum height. Based on the ordered pairs, this increase occurs between 0 seconds (60 feet) and 2 seconds (75 feet).
2. Height staying the same: The height of the water balloon stays the same between 2 seconds (75 feet) and 4 seconds (75 feet).
3. Height decreasing the fastest: The balloon's height begins to decrease after the peak. We determine the fastest decrease by finding the interval with the largest negative change in height over time. The largest drop is between 4 seconds (75 feet) and 6 seconds (40 feet).
4. The real-world constraints suggest that the water balloon cannot go below the ground level (0 feet). Thus, predicting the balloon's height at 16 seconds, it would remain at 0 feet as it has already hit the ground at 10 seconds and stays there afterward.