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Preparation for AF1.4

California Standards. Preparation for AF1.4 Solve problems manually by using the correct order of operations or by using a scientific calculator. Also covered: Preparation for AF1.3. Vocabulary. Power Exponent Base. A number produced by raising a base to an exponent.

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Preparation for AF1.4

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  1. California Standards Preparation forAF1.4 Solve problems manually by using the correct order of operations or by using a scientific calculator. Also covered: Preparation for AF1.3

  2. Vocabulary Power Exponent Base A number produced by raising a base to an exponent. The number that tells how many times to use the base as a factor in a power (the top #). When a number is written as a power, the number that is used as a factor (the bottom #).

  3. A DNA molecule makes a copy of itself 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.

  4. This multiplication can also be written as a power, using a base and an exponent. The exponent tells how many times to use the baseas a factor. Exponent 2 4 = 16 2  2  2  2 = Base

  5. Example 1: Evaluating Powers Find each value. A. 44 Use 4 as a factor 4 times. 44 = 4  4  4  4 = 256 B. 73 Use 7 as a factor 3 times. 73 = 7  7  7 = 343 C. 191 191 = 19 Use 19 as a factor 1 time. = 19

  6. To express a whole number as a power, write the number as the product of equal factors. Then write the product using the base and an exponent. For example, 10,000 = 10  10  10  10 = 104.

  7. Example 2: Expressing Whole Numbers as Powers Write each number using an exponent and the given base. A. 625, base 5 5 is used as a factor 4 times. 625 = 5  5  5  5 = 54 B. 64, base 2 2 is used as a factor 6 times. 64 = 2  2  2  2  2  2 = 26

  8. Example 3: Application 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 will learn the secret on Friday? On Monday, 3 people know the secret. On Tuesday, 3 times as many people know as those who knew on Monday. On Wednesday, 3 times as many people know as those who knew on Tuesday. On Thursday, 3 times as many people know as those who knew on Wednesday.

  9. Example 3 Continued On Friday, 3 times as many people know as those who knew on Thursday. Each day the number of people is 3 times greater. 3  3  3  3  3 = 35 = 243 On Friday 243 people will learn the secret. (Erik is not included --learn)

  10. Check It Out! 1. Find each value. 33 Use 3 as a factor 3 times. 33 = 3  3  3 = 27 2. Write the number using an exponent and the given base. 2,401, base 7 7 is used as a factor 4 times. 2,401 = 7  7  7  7 = 74

  11. Check It Out! 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 the first turn, she had 2 points. After the second turn, she would have 4 points. After the third turn, she would have 8 points. After each turn, her point total is 2 times greater. 2  2  2  2 = 24 = 16 points

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