1. Hot Air Balloon Investigation
Retrieved from Tina Franzen

2. Ginger and Paul want to ride in a hot air balloon
Ginger and Paul want to ride in a hot air balloon. Their trip can be described by the following function:
h(t) = t t3 – t t
where the height, h meters, of the balloon is relative to the ground for t hours.

3. Change the WINDOW Settings
Since time is along the x-axis, and we do not have a negative time, set X MIN = 0.
The ride will not take more than 5 hours so set X MAX = 5.
Since the height of the balloon is relative to the ground, we will not go below the ground level. Set Y MIN = 0.

4. Graph it!
Press the Y = button & type in the following equation:
-1.252x^ x^ x^ x
Press the GRAPH button.

5. What Does the Graph Show Us?
The graph starts off at the origin. Why?
Describe what is happening on the trip from the beginning to the end.

6. What Does the Graph Show Us?
What is the maximum height that the hot air balloon reached?
When did the balloon reach its maximum height?
How long did the trip last? How do you know?
What type of function would best describe this graph?