<
>
• 13. Gravity on the Moon

An object is dropped from a height of 50 feet on the moon. The table shows the distances it has fallen at various times.

Determine whether the pattern in the table is linear, exponential, quadratic, or none of these. Explain your reasoning. (See Example 5 and Example 6.)

• Worked-Out Solution

Use a spreadsheet to analyze the data.

The first differences are not equal, so the pattern is not linear.

The consecutive ratios are not equal, so the pattern is not exponential.

The second differences are equal. So, the pattern is quadratic.

These comments are not screened before publication. Constructive debate about the information on this page is welcome, but personal attacks are not. Please do not post comments that are commercial in nature or that violate copyright. Comments that we regard as obscene, defamatory, or intended to incite violence will be removed. If you find a comment offensive, you may flag it.

```  _  __     ___      ______   __   __   ______
| |/ //   / _ \\   /_   _//  \ \\/ // |      \\
| ' //   | / \ ||  `-| |,-    \ ` //  |  --  //
| . \\   | \_/ ||    | ||      | ||   |  --  \\
|_|\_\\   \___//     |_||      |_||   |______//
`-` --`   `---`      `-`'      `-`'   `------`

```
• 14. Gravity on Venus

An object is dropped from a height of 150 feet on Venus. The table shows the distances it has fallen at various times.

Determine whether the pattern in the table is linear, exponential, quadratic, or none of these. Explain your reasoning. (See Example 5 and Example 6.)

These comments are not screened before publication. Constructive debate about the information on this page is welcome, but personal attacks are not. Please do not post comments that are commercial in nature or that violate copyright. Comments that we regard as obscene, defamatory, or intended to incite violence will be removed. If you find a comment offensive, you may flag it.

```  ______    _____                ___      ______
/_   _//  |  ___||   ____      / _ \\   /_   _//
`-| |,-   | ||__    |    \\   / //\ \\    | ||
| ||    | ||__    | [] ||  |  ___  ||  _| ||
|_||    |_____||  |  __//  |_||  |_|| /__//
`-`'    `-----`   |_|`-`   `-`   `-`  `--`
`-`
```
• 15. Gravity on Mars

An object is dropped from a height of 300 feet on Mars. The table shows the distances it has fallen at various times.

Determine whether the pattern in the table is linear, exponential, quadratic, or none of these. Explain your reasoning. (See Example 5 and Example 6.)

• Worked-Out Solution

Use a spreadsheet to analyze the data.

The first differences are not equal, so the pattern is not linear.

The consecutive ratios are not equal, so the pattern is not exponential.

The second differences are equal. So, the pattern is quadratic.

These comments are not screened before publication. Constructive debate about the information on this page is welcome, but personal attacks are not. Please do not post comments that are commercial in nature or that violate copyright. Comments that we regard as obscene, defamatory, or intended to incite violence will be removed. If you find a comment offensive, you may flag it.

``` _____     __   __   __   __     ___     __   _
|  __ \\   \ \\/ //  \ \\/ //   / _ \\  | || | ||
| |  \ ||   \ ` //    \   //   | / \ || | '--' ||
| |__/ ||    | ||     / . \\   | \_/ || | .--. ||
|_____//     |_||    /_//\_\\   \___//  |_|| |_||
-----`      `-`'    `-`  --`   `---`   `-`  `-`

```
• 16. Gravity on Jupiter

An object is dropped from a height of 1600 feet on Jupiter. The table shows the heights of the object at various times.

Determine whether the pattern in the table is linear, exponential, quadratic, or none of these. Explain your reasoning. (See Example 5 and Example 6.)

These comments are not screened before publication. Constructive debate about the information on this page is welcome, but personal attacks are not. Please do not post comments that are commercial in nature or that violate copyright. Comments that we regard as obscene, defamatory, or intended to incite violence will be removed. If you find a comment offensive, you may flag it.

```  ______   _    _    _    _     ______
/_   _// | || | || | \  / ||  /_   _//     ___
| ||   | || | || |  \/  ||   -| ||-     /   ||
_| ||   | \\_/ || | .  . ||   _| ||_    | [] ||
/__//     \____//  |_|\/|_||  /_____//    \__ ||
`--`       `---`   `-`  `-`   `-----`      -|_||
`-`
```
• 17. Sign of the Second Differences

Graph the data in Exercises 14 and 15 on the same coordinate plane. Compare the graphs. What appears to be the relationship between the sign of the second differences and the corresponding graph?

Table from Exercise 14: Object dropped on Venus

Table from Exercise 15: Object dropped on Mars

• Worked-Out Solution

Use a spreadsheet to analyze the data.

For Exercise 14, the data values are increasing and the second differences are positive.

For Exercise 15, the data values are decreasing and the second differences are negative.

These comments are not screened before publication. Constructive debate about the information on this page is welcome, but personal attacks are not. Please do not post comments that are commercial in nature or that violate copyright. Comments that we regard as obscene, defamatory, or intended to incite violence will be removed. If you find a comment offensive, you may flag it.

```            _____     ______     ___      ______
____     |  ___||  /_   _//   / _ \\   /_   _//
|    \\   | ||__    `-| |,-   / //\ \\  `-| |,-
| [] ||   | ||__      | ||   |  ___  ||   | ||
|  __//   |_____||    |_||   |_||  |_||   |_||
|_|`-`    `-----`     `-`'   `-`   `-`    `-`'
`-`
```
• 18. Comparing Gravitational Forces

The moon's gravitational force is much less than that of Earth. Use the table in Exercise 13 and the table in Example 5 to estimate how many times stronger Earth's gravitational force is than the moon's gravitational force. Explain your reasoning.

Table from Example 5: Object dropped on Earth

Table from Exercise 13: Object dropped on the moon

These comments are not screened before publication. Constructive debate about the information on this page is welcome, but personal attacks are not. Please do not post comments that are commercial in nature or that violate copyright. Comments that we regard as obscene, defamatory, or intended to incite violence will be removed. If you find a comment offensive, you may flag it.
```  _____      ___    __    __   __   __    _____