8.1 Multiplication Properties of Exponents Objectives 1. Use properties of exponents to multiply exponential expressions.

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1 8.1 Multiplication Properties of Exponents Objectives 1. Use properties of exponents to multiply exponential expressions. 2. Use powers to model real life problems. Multiplication Properties of Exponents Let a and b be numbers and let m and n be positive integers. Product of Powers Property To multiply powers having the same the base, add the exponents. = Examples: = = Power of a Power Property To find the power of a power, multiply the exponents. = Examples: = = Power of a Product Property To find the power of a product, find the power of each factor and multiply. = Examples: = = Using the Product of Powers Property

2 Use the Power of a Power Property [ ] [ ] Using the Power of a Product Property Using All Three Properties A multiple choice test has two parts. There are 4 3 ways to answer the three questions in Part A. There are 4 7 ways to answer the seven questions in Part B. How many ways are there to answer all 10 questions? If you guess each answer. What is the probability you will get them all right?

3 8.2 Zero and Negative Exponents Objectives 1. Evaluate powers that have zero and negative exponents. 2. Graph exponential functions. Key Terms Exponential Function Definition of Zero and Negative Exponents. Let a be a nonzero number and let n be a positive integer. A nonzero number to the zero power is 1. a 0 = 1, a 0. is the reciprocal of. =, a 0. Powers with Zero and Negative Exponents ( ) Rewrite with positive exponents. Evaluate the Expression. Evaluate. ( )

4 Rewrite the expression with positive exponents. Graphing an Exponential Function. Graph the function y = 3 x. x y Graph the function y = ( ). x y

5 8.3 Division Properties of Exponents Objectives 1. Use the division property of exponents to evaluate powers and simplify expressions. 2. Use the division properties of exponents to model real life problems. Division Properties of Exponents Let a and b be numbers and let m and n be positive integers. Quotient of Powers Property To divide powers having the same base, subtract the exponents. =, Example: = = Power of a Quotient Property To find a power of a quotient, find the power of the numerator and the power of the denominator and divide. ( ) =, Example: ( ) = ( ) = Using the Quotient of Powers Property Using the Power of a Quotient Property Simplify the expression. ( ) ( ) ( )

6 Simplify the Expression. ( ) ( ) The average salary for a professional baseball player in the United States can be approximated by y=283, where t=0 represents Using this approximation, find the ratio of an average salary in 1988 to an average salary in 2010.

7 8.4 Scientific Notation Objectives 1. Use scientific notation to represent numbers. 2. Use scientific notation to represent real life situations. Key Terms Scientific notation Rewrite in Decimal Form. Rewrite in Scientific Notation. 52, ,000,000 Evaluate the expression. Write in the answer in scientific notation and in decimal form.

8 Light travels at a speed of 1.863x10 5 miles/second. How far does it travel in one year? In 1998, the population of the world was about 5.9 billion. In the same year, the population of the United States was 2.7 x What percent of the world population was the United States population?

9 8.5 Exponential Growth Functions Objectives 1. Write and use models for exponential growth. 2. Graph models for exponential growth. Key Terms Exponential Growth Exponential Growth Model C is the initial amount. (1 + r) is the growth factor. r is the growth rate. t is the time period. Compound Interest: You deposit $450 in an account that pays 2.5% interest compounded yearly. What is the balance in the account after 10 years? Your balance in an account that paid 5% annual interest compounded yearly for 5 years is $1250. What was the initial amount?

10 A population of 25 mice doubles each year for 4 years. What is the percent of increase of each year? What is the population after 4 years? A company starts with 20 employees and after one year it has 30. The company increases at the same rate every year for 6 years. What is the percent of increase each year? How many employees are there after 6 years?

11 8.6 Exponential Decay Functions Objectives 1. Write and use models for exponential decay. 2. Graph models for exponential decay. Key Terms Exponential Decay Exponential Decay Model C is the initial amount. (1 - r) is the decay factor. r is the decay rate. t is the time period. Depreciation: A car is purchased for $20,000. The value of the car will be less each year because of depreciation. The car depreciates (decrease in value) at the rate of 25% per year. Write an exponential decay model for this situation. What is the value of the car after 2 years? What is the value of the car after 4 years?

12 Graph the decay model from the previous example. t y Estimate the value of the car in 8 years? Classifying Models as Exponential Growth or Decay. Classify as exponential growth or decay. Identify the growth or decay factor. Identify the percent of increase or decrease for the time period. y = ( ) ( )