### 4.3 Exponential Decay

<
>
• 1. Exponential Decay of a Glacier

The size of a glacier is measured in the same way as land, in acres or hectares. In 1900, the size of a glacier was about 320 hectares. Between 1900 and 2000, its size decreased by about 14% per decade.

Write a formula that represents the size of the glacier at the beginning of each decade from 1900 to 2000.(See Example 1 and Example 2.)

• Worked-Out Solution

Use the general formula for exponential decay.

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.

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

```
Guest   10 years ago |
The photos on page 180 are shocking. How can people see photos like this a wonder about whether global warming is true or not?
1
• 2. Glaciers

The size of a glacier is measured in the same way as land, in acres or hectares. In 1900, the size of a glacier was about 320 hectares. Between 1900 and 2000, its size decreased by about 14% per decade. Make a table showing the size of the glacier at the beginning of each decade from 1900 to 2000. (See Example 1 and Example 2.)

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.

```   _____    ______             __   __    ______
/ ___//  /_   _//   ____     \ \\/ //  /_____//
\___ \\   -| ||-   |    \\    \ ` //   `____ `
/    //   _| ||_   | [] ||     | ||    /___//
/____//   /_____//  |  __//     |_||    `__ `
`-----`    `-----`   |_|`-`      `-`'    /_//
`-`                 `-`
```
• 3. Decrease in Area of a Glacier

The size of a glacier is measured in the same way as land, in acres or hectares. In 1900, the size of a glacier was about 320 hectares. Between 1900 and 2000, its size decreased by about 14% per decade. Sketch a graph showing the decrease in the area of the glacier from 1900 to 2000. (See Example 1 and Example 2.)

• Worked-Out Solution

The formula from Exercise 1 is

By entering this into a spreadsheet, you can draw the following graph.

Study Tip

1 square mile = 1 section = 4 quarters = 640 acres

1 hectare = 10,000 aquare meters

1 hectare = 2.47 acres

1 acre = 43,560 square feet (a square about 209 ft on each side)

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.

``` ______     ______   _    _     ______    _____
|      \\  /_   _// | || | ||  /_   _//  |__  //
|  --  //   -| ||-  | || | ||   -| ||-     / //
|  --  \\   _| ||_  | \\_/ ||   _| ||_    / //__
|______//  /_____//  \____//   /_____//  /_____||
`------`   `-----`    `---`    `-----`   `-----`

```
• 4. Estimating Area of a Glacier

The size of a glacier is measured in the same way as land, in acres or hectares. In 1900, the size of a glacier was about 320 hectares. Between 1900 and 2000, its size decreased by about 14% per decade. Use the graph in Exercise 3 to estimate the area of the glacier in 2000. (See Example 1 and Example 2.)

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.

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

```
• 5. Glacier

The size of a glacier is measured in the same way as land, in acres or hectares. In 1900, the size of a glacier was about 320 hectares. Between 1900 and 2000, its size decreased by about 14% per decade. A general rule is that a moving piece of ice and snow is called a glacier when its size is at least 10 hectares. Assuming the trend continues, when will the glacier be too small to be considered a glacier? ( See Example 1 and Example 2.)

• Worked-Out Solution

The formula from Exercise 1 is

A spreadsheet using this formula is shown below.

From the spreadsheet, you can see that the size will be too small to be classified as a glacier around 2130.

Study Tip

1 square mile = 1 section = 4 quarters = 640 acres

1 hectare = 10,000 aquare meters

1 hectare = 2.47 acres

1 acre = 43,560 square feet (a square about 209 ft on each side)

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.

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

```
• 6. Size of a Glacier

The size of a glacier is measured in the same way as land, in acres or hectares. In 1900, the size of a glacier was about 320 hectares. Between 1900 and 2000, its size decreased by about 14% per decade. Suppose that a recent study predicts that the glacier will be completely melted by 2040. (See Example 1 and Example 2.)

1. Does this prediction agree with your answer in Exercise 5? What does the research suggest about the melting rate of the glacier after 2000?
2. When do you think an exponential model would be appropriate to model glacial melting? When do you think a linear model would be appropriate? Explain.

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.
```  _  __     ___     _    _      ___      _  _