Ron Larson
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4.1 Exponential Growth

4.1 Exponential Growth
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  • Math Help

    Note in Example 2 that n represents the number of foldings and not elapsed time. The relationship between the numbers of foldings and noodles, however, can be modeled by the formula for exponential growth.

    To make a spreadsheet similar to the one in Example 2, use the steps below. [Note that Step 6 uses the exponential growth formula given in Example 2, .]

    1. Enter the titles "Foldings, n" and "Number of Noodles" into Row 1.
    2. Enter 0 into cell A2.
    3. Enter the formula =A2 + 1 into cell A3.
    4. Select cell A3. From the Edit menu, choose Copy.
    5. Select cells A4 through A14. From the Edit menu, choose Paste.
    6. Enter the formula = 2^A2 into cell B2.
    7. Select cell B2. From the Edit menu, choose Copy.
    8. Select cells B3 through B14. From the Edit menu, choose Paste.
  • Consumer Suggestion

    Want to learn how to make your own noodles? Visit allrecipies.com to find pasta recipes, learn how to cook pasta, and watch a video on how to make your own homemade noodles.

  • Checkpoint Solution

    Using the Internet, you can find that the greatest possible distance from Earth to Pluto is about 4.5 trillion miles.

    For simplicity, assume Chef Mark is 6 feet tall and that his arm span is equal to his height. Then the length of each noodle is 6 feet.

    To convert feet to miles, multiply by the unit conversion factor (1 mile/5280 feet).

    The steps for creating the spreadsheet in Example 2 are given in the Math Help. Use the steps below to extend the spreadsheet to 46 foldings and add a third column to track the length of the noodles.

    1. Select cells A14 and B14. From the Edit menu, choose Copy.
    2. Select cells A15 through B48. From the Edit menu, choose Paste.
    3. Enter the title "Length of Noodles (in miles)" into cell C1.
    4. Enter the formula =B2*6/5280 into cell C2.
    5. Select cell C2. From the Edit menu, choose Copy.
    6. Select cells C3 through C48. From the Edit menu, choose Paste.

    data folder

    From the spreadsheet, you can see that at 42 foldings the length of the noodles is 4,997,780,126 miles, which is greater than the greatest possible distance from Earth to Pluto.

    So the claim is true, 46 doublings of the noodles are "long enough to stretch to Pluto and beyond."

  • Comments (2)

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    system user
    Guest   1 decade ago |
    There is an interesting story about folding a piece of paper 12 times. See http://pomonahistorical.org/12times.htm.
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    system user
    Ron Larson (author)1 decade ago |
    One of my favorite books was written by Philip and Phylis Morrison. It is called "Powers of Ten". You can see the photographs that are in the book at the Web site www.powersof10.com/. Start at 10 to the zero power. You will see a photograph of a man lying on blanket in a park. As you increase the power, you move away from the man, into the universe. As you decrease the power, you move into the man, to the world of the small.
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