### 7.1 Linear Patterns

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• 13. Absorbance of Light Using Blue No. 1

The figure shows light passing through a glass container that contains a substance. Absorbance is a unitless measure of the amount of light that a substance absorbs as light passes through it.

The table shows the absorbance of light with a wavelenght of 630 nanometers for a solution of the food dye Blue No.1 in a 1-centimeter glass container at various concentrations.

1. Describe the pattern of the absorbance values
2. Make a scatter plot of the data.
3. Predict the next absorbance value in the pattern.

(See Example 5 and Example 6.)

• Worked-Out Solution
1. Each time the concentration increases by 1 milligram per liter, the absorbance increases by 0.164.
2. A scatter plot of the data is shown using a spreadsheet.

1. The next absorbance value in the pattern would be for a concentration of 5 milligrams per liter. The absorbance for this concentration should be

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

```
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• 14. Absorbance of Light Using Green No. 3

The figure shows light passing through a glass container that contains a substance. Absorbance is a unitless measure of the amount of light that a substance absorbs as light passes through it.

The table shows the absorbance of light with a wavelength of 625 nanometers for a solution of the food dye Green No. 3 in a 1-centimeter glass container at various concentrations.

1. Describe the pattern of the absorbance values.
2. Make a scatter plot of the data.
3. Predict the next absorbance value in the pattern.

(See Example 5 and Example 6.)

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

```
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• 15. Absorbance of Light Using Red No. 3

The figure shows light passing through a glass container that contains a substance. Absorbance is a unitless measure of the amount of light that a substance absorbs as light passes through it.

The table shows the absorbance of light with a wavelength of 527 nanometers for a solution of the food dye Red No. 3 with a concentration of 4 milligrams per liter in glass containers of various path lengths.

1. Describe the pattern of the absorbance values.
2. Make a scatter plot of the data.
3. Predict the next absorbance value in the pattern.

(See Example 5 and Example 6.)

• Worked-Out Solution
1. Each time the path length increases by 0.2 centimeter, the absorbance increases by 0.088.
2. A scatter plot of the data is shown using a spreadsheet.

1. The next absorbance value in the pattern would be for a path length of 1 centimeter. The absorbance for this path length should be

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

```
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• 16. Absorbance of Light Using Red No. 40

The figure shows light passing through a glass container that contains a substance. Absorbance is a unitless measure of the amount of light that a substance absorbs as light passes through it.

The table shows the absorbance of light with a wavelength of 500 nanometers for a solution of the food dye Red No. 40 with a concentration of 5 milligrams per liter in glass containers of various path lengths.

1. Describe the pattern of the absorbance values.
2. Make a scatter plot of the data.
3. Predict the next absorbance value in the pattern.

(See Example 5 and Example 6.)

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```__    __     ___      ______     ___      _  _
\ \\ / //   / _ \\   /_____//   / _ \\   | \| ||
\ \/ //   / //\ \\  `____ `   | / \ ||  |  ' ||
\  //   |  ___  || /___//    | \_/ ||  | .  ||
\//    |_||  |_|| `__ `      \___//   |_|\_||
`     `-`   `-`  /_//       `---`    `-` -`
`-`
```
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• 17. Absorbance of Light Using Yellow No. 5

The figure shows light passing through a glass container that contains a substance. Absorbance is a unitless measure of the amount of light that a substance absorbs as light passes through it.

The absorbance of light with a wavelength of 428 nanometers for a solution of the food dye Yellow No. 5 in a 1-centimeter glass container is proportional to the concentration of Yellow No. 5. The absorbance of a solution with a concentration of 2 milligrams per liter is 0.106. What is the absorbance of a solution with a concentration of 5 milligrams per liter? (See Example 5 and Example 6.)

• Worked-Out Solution

You are given that the absorbance is proportional to the concentration. You also know that

• when the concentration is 0, the absorbance is 0, and
• when the concentraiton is 2, the absorbance is 0.106.

This is enough information to determine that the absorbance increases by 0.053 each time the concentration increases by 1 milligram per liter. The spreadsheet shows that when the concentration is 5 milligrams per liter, the absorbance is 0.265.

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

```
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• 18. Absorbance of Light Using Yellow No. 6

The figure shows light passing through a glass container that contains a substance. Absorbance is a unitless measure of the amount of light that a substance absorbs as light passes through it.

The absorbance of light with a wavelength of 484 nanometers for a solution of the food dye Yellow No. 6 with a concentration of 6 milligrams per liter is proportional to the path length. The absorbance of the solution in a 0.5-centimeter glass container is 0.162. What is the absorbance of the solution in a 1.1-centimeter glass container? (See Example 5 and Example 6.)

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