### Home > CALC > Chapter Ch2 > Lesson 2.2.3 > Problem 2-81

A helium balloon is released from the ground and floats upward. The height of the balloon is shown at the following times: Homework Help ✎

**Time**(sec)0

1

2

3

4

5

6

7

8

9

10

**Height**(feet)0

50

98

144

188

230

270

308

344

378

410

What was the average velocity over the first 10 seconds of the balloon's flight? Over the first 5 seconds?

Find the finite differences for the heights. How is the velocity changing? Explore this using the 2-81 eTool (Desmos).

What do the finite differences tell you about the height function for the balloon?

In the case of the helium balloon.

average velocity between *t* = 0 and *t* = 10:

Now find the average velocity between *t* = 0 and *t* = 5.

This is an example of a finite difference table.

Use the eTool below to explore this.

Click on the link below to view the full version of the eTool. Calc 2-81 HW eTool

In this story, finite differences (Δ*y*) represent the average velocity over consecutive one second intervals.

Is the height of the balloon increasing, decreasing or both? How do finite differences help you answer this?