1. Objectives 1.) To review and solidify basic exponential expressions and equations for the purpose of further use in more complex exponential problems

2. Vocabulary A power is a number resulting from a number brought to an exponent. The parts of a power: Include a base number and an exponent. The base is based, while the exponent floats 5 3 = 125

3. Warm- up Solve the following perfect square problems: 1 2 =9 2 = 2 2 =10 2 = 3 2 =11 2 = 4 2 =12 2 = 5 2 =13 2 = 6 2 = 7 2 = 8 2 =

4. Quick Study Time Your skills on perfect squares, cubes, powers of 2 and powers of 3 will be tested. Cubed Powers: 1 3 =12 3 = 83 3 = 27 4 3 = 645 3 = 125 Base 2 Powers 2 1 = 22 2 = 42 3 = 8 2 4 = 162 5 = 322 6 = 64 Base 3 Powers 3 1 = 33 2 = 93 3 = 27 3 4 = 81

5. Definition of Exponential Equations Exponential functions are equations involving constants with exponents Notated: y = a x a= base; a>0 and not equal to 1 x = exponent/ power

6. Properties of exponents 1.) a 0 = 2.) a m a n = 3.) (ab) m =4.) (a n ) m = 5.)6.) 7.)

7. In-depth Look of Property # 6 Negative exponents Cross the line, flip the sign.

8. In- depth Look of Property #7 Radicals versus Rational Exponents... Can you solve the expression with your calculator?

9. Putting it all together 3.) (ab) m = a m a m 4.) (a n ) m = a nm 1.) a 0 = 12.) a m a n = a m+n Write the expression using positive rational exponent 5.)6.) 7.)

10. Graphs of Exponential Functions Pg. 200 Graphs of exponential functions x f(x) f(x) = a x, a>1 x f(x) f(x) = a x, a<1 f(x) = a -x

11. Characteristics of Exponential Function Graphs

12. Transformations

13. Compound interest

14. One lucky day, you find $8,000 on the street. At the Bank of Baker- that’s my bank, I am offering you an interest rate of 10% a year. Being the smart students you are, you invest your money at my bank. After the first year, your account collects 10% interest, so I would have to payout 8000+8000(.1)= $8,800 Or, 8,000(1 +.1) = $8,800 The second year, your $8,800 will collect even more interest and become 8,800(1 +.1) = 8,000(1 +.1)(1+.1)= $9,680

15. Complete the table below Year12345 Payout Amou nt 8,800 9,680 10,648 11, 71212,884 One lucky day, you find $8,000 on the street. At the Bank of Baker- that’s my bank. I am offering you an interest rate of 10% a year. Being the smart students you are, you invest your money at my bank.

16. Deal or No Deal? You come to me with $5000. I have an interest rate of 4.1 %. You want to establish this amount in my bank for 20 years. What if I compound your investment quarterly. I will apply a compounded interest rate 4 times but I will divide the interest rate by 4.

17. Initial investmen t Interest rate in decimal form I will pay 4 times per year for 20 years, but as consequence I will divide interest rate by 4 11,168.24 11,305.21

18. Compound interest

19. In 1683, mathematician Jacob Bernoulli considered the value of as n approaches infinity. His study was the first approximation of e

20. e= 2.71828182845904523546028747135266249 7757246093699959574077078727723076630 3535475945713821785251664274663919320 0305992181741349662904357290033829880 7531952510190115728241879307….. Comparable to an irrational number like ∏

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