Algebra I Chapter 7 Notes

1. Algebra I Chapter 7 Notes Rules of Exponents

2. Section 7-1 Monomial – Constant – Base – Exponent -

3. Section 7-1 Monomial – a number, a variable, or the product of a number and variable with non-negative, integer exponents Constant – a monomial that is a real number Base – term being multiplied in an exponential expression Exponent – the number of times the base is multiplied in an exponential expression

4. Section 7-1: Multiplication Rules of Exponents, Day 1 Ex) Determine whether each expression is a monomial. Write yes or no, explain WHY. a) 10 b) f + 24 c) d) e) -5y

5. Section 7-1: Multiplication Rules of Exponents, Day 1 Product of Powers Ex) Simplify each expression a) b) c)

6. Section 7-1: Multiplication Rules of Exponents, Day 1 Power of a Power Ex) Simplify a) b)

7. Section 7-1: Multiplication Rules of Exponents, Day 2 Power of a Product Ex) Simplify each expression a) b) c) d)

8. Section 7-1: Multiplication Rules of Exponents, Day 2 Ex) Use all rules to simplify a) b) c) d)

9. Section 7-2: Division Rules of Exponents, Day 1 Quotient of Powers Ex. Simplify a) b) c)

10. Section 7-2: Division Rules of Exponents, Day 1 Power of a Quotient Ex) Simplify a) b) c) d)

11. Section 7-2: Division Rules of Exponents, Day 1 Simplify using division rules of exponents 1) 2) 3) 4) 5) 6)

12. Section 7-2: Division Rules of Exponents, Day 2 Zero Exponent Property Ex) Simplify. Assume no denominator = zero a) b) c)

13. Section 7-2: Division Rules of Exponents, Day 2 Negative Exponent Property Ex) Simplify. NO NEGATIVE EXPONENTS! a) b) c) d)

14. Section 7-2: Division Rules of Exponents, Day 2 Simplify using division rules of exponents 1) 2) 3) 4)

15. Section 7-4: Scientific Notation Scientific Notation – a number written in the form , where 1 <a< 10 and n is an integer. Ex) Write the following numbers in scientific notation. 1) 201,000,000 2) 0.000051

16. Section 7-4: Scientific Notation Ex) Write the following numbers in standard form 1) 2)

17. Section 7-4: Multiplying with Scientific Notation Ex) Use rules of exponents to multiply the following numbers together. Express your answer in both scientific notation and standard form! 1) 2)

18. Section 7-4: Dividing with Scientific Notation Ex) Use rules of exponents to multiply the following numbers together. Express your answer in both scientific notation and standard form! 1) 2)

19. Section 7-5: Exponential Functions – Exponential Growth, Day 1 Exponential Function – A function that can be written in the form , where a cannot be 0, b > 0, and b cannot be 1. Examples of exponential functions: , , or Exponential Growth

20. Section 7-5: Exponential Functions – Exponential Growth, Day 1 Graph of Exponential Growth

21. Section 7-5: Exponential Functions – Exponential Growth, Day 1 Ex) Graph , Find the y-intercept, and state the domain and range. You will have to create a table to graph! What is the pattern on the table?

22. Section 7-5: Exponential Functions – Exponential Decay, Day 2 Exponential Decay

23. Section 7-5: Exponential Functions – Exponential Decay, Day 2 Graph of Exponential Decay

24. Section 7-5: Exponential Functions – Exponential Decay, Day 2 Ex) Graph , Find the y-intercept, and state the domain and range. You will have to create a table to graph! What is the pattern on the table?

25. Section 7-6: Exponential Growth and Decay Patterns, Day 1 Equation for Exponential Growth: a: initial amount t : time y: final amount r: rate of change expressed as a decimal, r > 0 Ex) The prize for a radio station contest begins with a $100 gift card. Once a day, a name is announced. The person has 15 minutes to call or the prize increases 2.5% for the next day. • Write an equation representing the amount of the gift card after t days with no winner • How much will the card be worth if no one claims it after 10 days?

26. Section 7-6: Exponential Growth and Decay Patterns, Day 1 Compound Interest – interest earned or paid on both the initial investment AND previously earned interest. It is an application of exponential growth. Equation for Compound Interest A: current amount P: principal/initial amount r: annual interest rate expressed as a decimal n: number of times interest is compounded per year t: time in years

27. Section 7-6: Exponential Growth and Decay Patterns, Day 1 Ex) Maria’s parents invested $14,000 at 6% per year compounded monthly. How much money will there be in the account after 10 years?

28. Section 7-6: Exponential Growth and Decay Patterns, Day 2 Equation for Exponential Decay a: initial amount y = final amount t: time r: rate of decay as a decimal 0 < r < 1 Ex) A fully inflated raft is losing 6.6% of its air every day. The raft originally contained 4500 cubic inches of air. • Write an equation representing the loss of air • Estimate the amount of air in the raft after 7 days

29. Section 7-6: Exponential Growth and Decay Patterns, Day 2 Solve the 3 problems. You must choose which equation to use on each. • Paul invested $400 into an account with 5.5% interest compounded monthly. How much will he have in 8 years? • Ms. Acosta received a job as a teacher with a starting salary of $34,000. She will get a 1.5% increase in her salary each year. How much will she earn in 7 years? • In 2000 the 2200 students attended East High School. The enrollment has been declining 2% annually. If this continues, how many students will be enrolled in the year 2015?