Transcript exponent
9/3/10 Exponents Entry Task You have just installed a water pond in your backyard. You intend to place water lilies in the pond. According to the package a water lily doubles in size every day. From the time you install the first lily until the entire surface of the pond is covered will take 20 days. How long will it take for the pond to be half covered? 19 days Today’s Plan: -Warm up -Exponents -Practice Learning Target: -I will represent numbers using exponents. 9/3/10 Exponents Multiplication Symbols 3·2 (3)(2) Today’s Plan: -Warm up -Exponents -Practice Learning Target: -I will represent numbers using exponents. 2-1 Exponents Simplify. 1. 2·2·2 2. 10 · 10 · 10 · 10 3. 5·5·5 4. 1 · 1 · 1· 1 · 1· 1 · 1 Course 2 8 10,000 125 1 2-1 Exponents A DNA molecule makes a copy of itself by splitting in half. Each half becomes a molecule that is identical to the original. The molecules continue to split so that the two become four, the four become eight, and so on. Each time DNA copies itself, the number of molecules doubles. After four copies, the number of molecules is 2 · 2 · 2 · 2 = 16. Course 2 2-1 Exponents This multiplication can also be written as a power, using a base and an exponent. The exponent tells how many times to use the base as a factor. Exponent Base “2 to the fourth power.” Course 2 2-1 Exponents Additional Example 1: Evaluating Powers Find each value. A. 43 4·4·4 64 B. 72 7·7 49 Course 2 4 to the third power (or 4 cubed) 7 to the second power (or 7 squared) 2-1 Insert Lesson Title Here Exponents Try This: Example 1 Find each value. A. Course 2 33 3·3·3 27 B. 62 6·6 36 2-1 Exponents Any number to the first power is equal to that number. 61 = 6 131 = 13 251 = 25 Any number to the zero power is equal to 1. 60 = 1 Course 2 100 = 1 190 = 1 2-1 Exponents On Monday, Erik tells 3 people a secret. The next day each of them tells 3 more people. If this pattern continues, how many people besides Erik will know the secret on Friday? Each day the number of people is 3 times greater. 3 · 3 · 3 · 3 · 3 = 35 = 243 On Friday 243 people besides Erik will know the secret. Course 2 2-1 Insert Lesson Title Here Exponents Try This: Example 3 In a game, a contestant had a starting score of one point. She doubled her score every turn for four turns. Write her score after four turns as a power. Then find her score. After each turn, her point total is 2 times greater. 2 · 2 · 2 · 2 = 24 = 16 points Course 2 2-1 Exponents Insert Lesson Title Here Find each value. 1. 73 3. 34 343 2. 63 4. 85 81 216 32,768 Write each number using an exponent and given base. 5. 125, base 5 6. 16, base 2 53 24 7. Find the volume of a cube if each side is 12 long. 1,728 in3 Course 2 inches 9/3/10 Exponents Assignment #1 Exponents: pg. 62 #10-21, 31 OR Challenge Assignment #1 Exponents: pg. 62 #36-45 Today’s Plan: -Warm up -Exponents -Practice Learning Target: -I will represent numbers using exponents.