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, 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? Part b: During what interval(s) of the domain is the water balloon's height staying the same? 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. Part d: Use the constraints of the real-world situation to predict the height of the water balloon at 10 seconds.

Answer 1

The water balloon's height is increasing from 0 to 2 seconds, remains constant at 80 feet from 2 to 3 seconds, decreases the fastest from 3 to 4 seconds, and is predicted to be at 0 feet at 10 seconds.

Step-by-step explanation:

To answer the questions about the linear model of the water balloon's height over time, we need to look at the ordered pairs provided and determine the intervals for the different behaviors of the balloon's height.

Part a: Height Increasing

The water balloon's height is increasing between the intervals where each successive time point reflects a higher value for height. In this case, the height is increasing from 0 to 2 seconds.

Part b: Height Constant

The height of the water balloon remains the same at 80 feet from 2 to 3 seconds, indicating the height is staying the same during this interval.

Part c: Height Decreasing Fastest

The height is decreasing the fastest where the slope of the height vs. time graph is steepest in the negative direction. This occurs between 3 to 4 seconds as the height drops from 80 feet to 20 feet.

Part d: Prediction at 10 seconds

Using the constraints of this real-world situation, after 6 seconds, the water balloon has hit the ground (0 feet). Therefore, at 10 seconds, the water balloon would also be at a height of 0 feet, as it cannot go below the ground level.