Hot Air Balloon Investigation

1
Hot Air Balloon Investigation

• PPT 5.3.1

2
Introduction

• Two students, Ginger and Paul, were going on a
  hot air balloon trip to see what it was like.
• Their trip can be described by the function
• h(t) -1.252t4 10.732t3 30.377t2 29.931t
• where the height, h metres, of the balloon is
  relative to the ground for t hours.

3
Graph the Trip

• We are going to graph the equation given on the
  previous slide on your graphing calculator.
• Before we enter the equation, we are going to
  change your WINDOW settings.

4
WINDOW Settings

• Since time is along the x-axis, and we dont have
  a negative time, set X MIN 0.
• The ride will most likely not take more than 5
  hours, so set X MAX 5.
• Since the height of the balloon is relative to
  the ground, we would not expect it to go below
  the ground level, so we can set Y MIN 0.
• Your screen should look like the one on the
  right.

5
Graph it!

• Okay, now we are ready to graph the equation.
• Press the Y button and type in the following
• -1.252x410.732x3-30.377x229.931x
• Press the GRAPH button.
• Your screen should look like the one on the
  right.

6
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.
Approximately, what is the maximum height that
the hot air balloon reaches?
At what time did the balloon reach its maximum
height?
How long did the trip last? How do you know?
What type of function would be the best to
describe this graph?