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 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. Use complete sentences to support your answer. (3 points)

Answer 1

The water balloon is decreasing the fastest at the interval [4, 6]

The predicted height of the water balloon at 16 seconds will be 0 feet

How to determine the fastest decreasing interval

The fastest decreasing interval is the interval that has the highest magnitude of negative slope.

This will be the steepest part of the line that is slanting downward from left to right.

Examining the graph shows that the interval is within 4 to 6

For the height of the water balloon after 16 seconds, the water balloon will always float and will not have a negative value. At 16 seconds, if the balloon is still there, it will still be floating. The height at this point is 0 km.