PlEASE HELP MEE ASAP 50 PTS 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:

Time (In seconds)
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 16 seconds. Use complete sentences to support your answer.

The data for linear pair are;

The domain are the values (input) on the x-axis which is the time

The range are the values input on the y-axis which is the height reached by the balloon

Part A

The interval of the domain during which the water balloon height is increasing is 0 ≤ x ≤ 2

Part B

The intervals of the domain the water balloon’s height stays the same are;

2 ≤ x ≤ 3 and 6 ≤ x ≤ 8

Part C

The water balloon height is decreasing at the following intervals;

At the interval 3 ≤ x ≤ 4

The rate of decrease = (20 ft. – 80 ft.)/(4 s – 3 s) = -20 ft./s.

At the interval 4 ≤ x ≤ 6

The rate of decrease = (0 ft. – 20 ft.)/(6 s – 4 s) = -10 ft./s

Therefore, the interval of the domain that the balloon’s height is decreasing the fastest is 3 ≤ x ≤ 4

Part D

According to Newton’s law of motion, provided that the no additional force is applied to the the balloon, at 10 seconds, the height of the water balloon is 0 ft. given that the height of the balloon is constantly decreasing from 3 seconds after being thrown off the roof, reaching a height of 0ft. at 6 seconds and maintaining that height up until 8 seconds.

By extending the graph further, the height of 0 ft. is obtained at 10 seconds after the balloon is thrown