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:


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)

Answer 1

A. An increasing lines goes up from left to right. This is shown from 0 to 2

B. A horizontal line would show the height remaining the same. This is shown from 2 to 3

C. The steeper the line the faster the decrease. This is shown from 3 to 4

D. The height of the balloon at 10 seconds would be 0 as it hits the zero mark at 6 seconds and the arrow continues along the 0 line.

Answer 2

Answer:

see below

Step-by-step explanation:

Part A  the balloons height is increasing when the line is going up

It is increasing between 0 and 2

0 ≤t≤2

Part B  the balloons height remains the same when the line is flat

It is constant between 2 and 3

2 ≤t≤3

Part C  the balloons height is decreasing when the line is going down

It is decreasing the fastest when the line is going down the quickly and that is between 3 and 4.  The slope is (80-20)/(4-3) = 60/1 = 60.  The larger the slope, the faster the height decreases.

3 ≤t≤4

Part D  At 10 second the balloon will be on the ground.  At 6 second the height is zero and remains at 0.