In previous sections of this resource, you learned that a rate of change for a linear function is also called the slope of the line for a linear function. However, in the real world, not all relationships are linear. In this section, you will investigate a situation that combines both linear and non-linear relationships – the height of a hot air balloon versus time.

Directions:

1. Use this link to complete the activity.
2. Check the Show Balloon/Animation Control and Visualize Average Rate of Change boxes located in the upper right hand corner.
3. Click the Play button in the lower left hand corner of the applet to watch the balloon rise and fall.

Use the applet to answer the following questions.

1. What is the average rate of change of the balloon’s height? Between 0 and 10 minutes? 10 and 20 minutes? (Hint: Move the red dots to the designated times. Look at the formula below the graph to determine your answer.)

   Interactive popup. Assistance may be required.

   Check Your Answer

   Between 0 and 10 minutes, the average rate of change is 18.34 ft/min. Between 10 and 20 minutes, the average rate of change is -1.67 ft/min.

2. How would you describe the parts of the graph where the balloon is rising and falling?

   Interactive popup. Assistance may be required.

   Check Your Answer

   As the balloon rises, the graph rises, or increases. As the balloon falls, the graph falls, or decreases.