### 4.1-4.2 Quiz

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• 1. Average Inflation Rate

From 1983 to 2010, the average annual inflation rate in the United States was about 3%. Write a formula that can be used to model the exponential growth of the consumer price index from 1983 to 2010.

• Worked-Out Solution

Use the general formula for exponential growth.

P = 100,  r = 3%,  n is measured in years with n = 0 representing 1983

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

```
• 2. Modeling the Consumer Price Index

From 1983 to 2010, the average annual inflation rate in the United States was about 3%. Use the formula from Exercise 1 and a spreadsheet to project the consumer price index from 1983 to 2020.

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

```
• 3. Modeling the Consumer Price Index

Use a spreadsheet to create a double bar graph to compare the projected consumer price index to the actual consumer price index from 1983 to 2010.

• Worked-Out Solution

From Exercise 1, a model for the consumer price index is

P = 100,  r = 3%,  n is measured in years with n = 0 representing 1983

By entering the actual CPI together with this formula into a spreadsheet, you can obtain the following graph.

Overall, the formula models the actual consumer price index fairly well. It is somewhat off in the 1990s because 1990 and 1991 were years of high inflation.

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```  _____     ______               ___      _____
/  ___||  /_   _//   ____      / _ \\   |__  //
| // __     -| ||-   |    \\   / //\ \\    / //
| \\_\ ||   _| ||_   | [] ||  |  ___  ||  / //__
\____//   /_____//  |  __//  |_||  |_|| /_____||
`---`    `-----`   |_|`-`   `-`   `-`  `-----`
`-`
```
• 4. Expected Value

From 1983 to 2010, the average annual inflation rate in the United States was about 3%. You buy a new car for \$25,000 in 2010. Using the actual CPI for 2010, what would you expect to pay for a new car with similar features in 2020?

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

```
• 5. Black Tuesday

On "Black Tuesday", October 29, 1929, the stock market lost over \$14 billion. Estimate this loss in terms of 2020 dollars. The consumer price index for 1929 is 17.1.

• Worked-Out Solution

The projected consumer price index for 2020 is

Because the CPI was 17.1 in 1929, you can estimate that \$14 billion in 1929 would be worth

in 2020. In other words, the loss would be almost a quarter of a trillion dollars.

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

```
• 6. Investment

You invest \$10,000 in 2005. Your investment earns an average of 2% annually for 15 years. In 2020, is the buying power of your investment higher than in 2005? Explain your reasoning.

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``` ______    __   __    _____     ______   ______