### 10.2 The Olympics

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• 1. Describing Patterns in Men's Olympic Discus Throw

Describe any patterns in the graph. (See Example 1 and Example 2.)

• Worked-Out Solution

Except for 1920, 1972, 1984, 1992, 2000, and 2008, the winning distance has increased each year. In recent Olympics, the winning distance has leveled off around the 70-meter mark.

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

```
• 2. Concrete Discus Introduced

The concrete throwing circle was introduced to the Olympic discus throw in 1954. Discuss the impact of the concrete throwing circle on the winning distances. (See Example 1 and Example 2.)

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

```
• 3. Men's Discus Throw in the 1940 Olympics

The Olympics were not held in 1940 or 1944 because of World War II. Based on the graph, what do you think the winning distance would have been in 1940 if the Olympics had been held? Explain your reasoning. (See Example 1 and Example 2.)

• Worked-Out Solution

From the graph, you can see that the winning distance increased in each of the Olympics from 1924 through 1936. Had the 1940 Olympics been held, the winning distance likely would have been between 50 and 55 meters. Visually, a distance in this range makes sense.

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

```
• 4. Expectation for 2012 Olympics

What is a reasonable expectation for the winning distance in the 2012 Olympics? Explain your reasoning. (See Example 1 and Example 2.)

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

```
• 5. Graphing Winning Distances for Women's Discus Throw

The winning distances for the women's discus throw are shown.

(1928, 39.62), (1932, 40.58), (1936, 47.63), (1948, 41.92), (1952, 51.42),
(1956, 53.69), (1960, 55.10), (1964, 57.27), (1968, 58.28), (1972, 66.62),
(1976, 69.00), (1980, 69.96), (1984, 65.36), (1988, 72.30), (1992, 70.06),
(1996, 69.66), (2000, 68.40), (2004, 67.02), (2008, 64.74)

Sketch a graph of the winning distances. Describe any patterns in the graph. (See Example 1.)

• Worked-Out Solution

Using a spreadsheet, you can make a scatter plot of the winning distances for the women's discus throw.

The winning distance increased in every Olympics from 1952 through 1980. The current Olympic record was set in 1988. From 1992 through 2008, the winning distance has decreased in every Olympics.

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

```
• 6. Graphing the Olympic Records for Women's Discus Throw

The winning distances for the women's discus throw are shown.

(1928, 39.62), (1932, 40.58), (1936, 47.63), (1948, 41.92), (1952, 51.42),

(1956, 53.69), (1960, 55.10), (1964, 57.27), (1968, 58.28), (1972, 66.62),

(1976, 69.00), (1980, 69.96), (1984, 65.36), (1988, 72.30), (1992, 70.06),

(1996, 69.66), (2000, 68.40), (2004, 67.02), (2008, 64.74)

Sketch a graph that shows the Olympic record for each of the years in the data set. (See Example 1.)

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