Investigation 1.1

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).