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Explore Exponential Growth and Form with Paper and Calculator

Discover the fascinating world of exponential growth through simple paper cutting exercises and converting long multiplied numbers into exponential form. Learn how to predict patterns and use calculators effectively.

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Explore Exponential Growth and Form with Paper and Calculator

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  1. Investigation 1.1 Exponential Growth

  2. Take a sheet of paper. Cut it in half. • Stack them and cut in half again. • Repeat the process. • Fill in the table.

  3. 1 2 3 4 5 6 2 4 8 16 32 64 Cuts (x)Pieces of Paper (y) Can you see the pattern of change in y? Predict the pieces of paper for the 10th cut.

  4. 10th cut 1,024 20th cut  1,048,576 30th cut  1,073,741,824 How many cuts to get 500 pieces of paper? 9 cuts = 512

  5. Investigation 1.2 Exponential Form a simpler way to write long strings of the same multiplied numbers like 2 x 2 x 2 x 2 = 16 we can write as24

  6. Exponential Form Exponent 25 Base

  7. Expanded Form To write this in Expanded Form, just write the long string of numbers. 25 Five twos – and the exponent is a 5. See the connection? 2 x 2 x 2 x 2 x 2

  8. Write in Exponential Form 2 x 2 x 2 x 2 = 24 55 5 x 5 x 5 x 5 x 5 = 1.56 1.5 x 1.5 x 1.5 x 1.5 x 1.5 x 1.5 =

  9. Write in Expanded Form 33 = 3 x 3 x 3 5.24 = 5.2 x 5.2 x 5.2 x 5.2

  10. Standard Form • The way we usually see numbers. 27 is the standard form of 33 or 3 x 3 x 3 Exponential Form Expanded Form

  11. Your CalculatorYou brought it today, right? • Calculators have different ways of doing Exponents. • Look for a yx key or a karat key  • In both cases, enter the base first and then the exponent key, then the exponent (or power).

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