1. UNIT 3: EXPONENTS, RADICALS, AND EXPONENTIAL EQUATIONS Final Exam Review

2. TOPICS TO COVER  Exponent Rules  Converting Radicals to Fractional Exponents  Converting Fractional Exponents to Radicals  Exponential Growth and Decay  Word Problems

3. EXPONENT RULES  Mathematical Expressions can be simplified used exponent rules  Here are all of the rules:  ADDING AND SUBTRACTING EXPRESSIONS  MULTIPLYING EXPRESSIONS  RAISING A POWER TO A POWER  DIVIDING EXPRESSIONS  NEGATIVE EXPONENTS  ZERO EXPONENTS

4. ADDING AND SUBTRACTING EXPRESSIONS  When you are adding and subtracting exponents, you must:  COMBINE LIKE TERMS only!  Make sure to DISTRIBUTE the NEGATIVE when subtracting  Example: (4x 2 + 9x – 6) + (7x 2 – 2x – 1) = 11x 2 + 7x – 7 (3x 2 + 5x – 8) – (5x 2 – 4x + 6) = -2x 2 + 9x – 14

5. MULTIPLYING EXPRESSIONS  When you are multiplying expressions  MULTIPLY the whole numbers  ADD the exponents  Example: (4x 3 )(2x 2 ) = 8x 5 (-4x 5 )(3x 2 ) = -12x 7

6. RAISING A POWER TO A POWER  When you are raising a power to a power:  RAISE the whole numbers to the power  MULTIPLY the exponents  Example: (5x 2 ) 4 = 625x 8 (-3x 6 ) 3 = -27x 18

7. DIVIDING EXPRESSIONS

8. NEGATIVE EXPONENTS

9. ZERO EXPONENTS

10. PRACTICE ALL EXPONENT RULES

11. CONVERTING A RADICAL INTO A FRACTIONAL EXPONENT

13. CONVERTING A FRACTIONAL EXPONENT INTO A RADICAL

15. EXPONENTIAL GROWTH AND DECAY  Exponential Functions can either represent GROWTH or DECAY  Every function follows this formula:  y = a b x  a is the INITIAL value  b is the GROWTH or DECAY rate  If the problem is growth, use (1 + rate) for b  If the problem is decay, use (1 – rate) for b  x is the TIME

16. EXPONENTIAL GROWTH AND DECAY  Example Write the equation for this situation: The amount of movies made in 2015 was 1,255. The number is expected to increase by 2.1% every year. Answer: y = 1255(1 + 0.021) x

17. EXPONENTIAL GROWTH AND DECAY  Now thy these Write an equation for these situations: 1.The population of an ant colony with 5,056 members increases by 5.6% every year. 2.The number of people who live in North Dakota (who currently has 739,482 people) decreases every year by 1.3%.

18. WORD PROBLEMS  There are many real life situations that use exponential growth and decay. You can use these equations in order to predict outcomes in the future.  In order to do this, use your calculator to put in the equation and use the table to find values.

19. WORD PROBLEMS  Try this one: The model y = 604000(1 + 0.045) x represent the population of Washington DC after 1990. 1. Find the initial population 2. Is this a growth or decay problem? 3. Predict the population in 1995. 4. In what year will the population reach 1,000,000?

20. ALL DONE