1. Holt Geometry 3-1 Lines and Angles A-SSE.A.1bInterpret expressions that represent a quantity in terms of its context. Interpret complicated expressions by viewing one or more of their arts as a single entity. A-CED.A.2Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. F-IF.C.7eGraph functions expressed symbolically, and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

2. Holt Geometry 3-1 Lines and Angles  Asymptote  Decay factor  Exponential decay  Exponential function  Exponential growth  Growth factor

3. Holt Geometry 3-1 Lines and Angles  Paper for notes  Graph paper  Pearson 7.1  Graphing Calc.

4. Holt Geometry 3-1 Lines and Angles TOPIC: 7.1 Exploring Exponential Models Name: Daisy Basset Date : Period: Subject: Notes Objective: Graph exponential functions.

5. Holt Geometry 3-1 Lines and Angles Vocabulary  Exponential Function (draw the graph and labels)  Exponential Growth  Exponential Decay  Asymptote  Growth Factor  Decay Factor

6. Holt Geometry 3-1 Lines and Angles 1. Make a table of values and graph each.

7. Holt Geometry 3-1 Lines and Angles A. y = 2 x x2x2x y -4 -3 -2 0 1 2 3 2 -4 0.0625 2 -3 2 -2 2323 2 2121 2020 2 -1 0.125 0.25 0.5 1 2 4 8

8. Holt Geometry 3-1 Lines and Angles 2. Identify each function or situation as an example of exponential growth or decay. What is the y-intercept?

9. Holt Geometry 3-1 Lines and Angles A. y = 12(0.95) x a b Since, a and, the function represents exponential. >0 0<b<1 decay

10. Holt Geometry 3-1 Lines and Angles y = 12(0.95) x y-intercept (, ) 0 12 y = 12(0.95) 0

11. Holt Geometry 3-1 Lines and Angles B. y = 0.25(2) x a b Since, a and, the function represents exponential. > 0b > 1 growth

12. Holt Geometry 3-1 Lines and Angles y = 0.25(2) x y-intercept (0, )0.25 y = 0.25(2) 0

13. Holt Geometry 3-1 Lines and Angles C.You put $1000 into a college savings account for 4 years. The account pays 5% interest annually.

14. Holt Geometry 3-1 Lines and Angles The amount of money in the bank grows 5% annually. It represents exponential growth.

15. Holt Geometry 3-1 Lines and Angles The y-intercept represents the amount of _____ at _______, which is the initial investment. money time = 0

16. Holt Geometry 3-1 Lines and Angles The y-intercept is,, which is the dollar value of the initial investment. $1000

17. Holt Geometry 3-1 Lines and Angles 3. You invested $1000 in a savings account at the end of 6 th grade. The account pays 5% annual interest.

18. Holt Geometry 3-1 Lines and Angles How much money will be in the account after six years? A(t) = a(1 + r) t

19. Holt Geometry 3-1 Lines and Angles A(t) = a = r = t = A(t) = a(1 + r) t initial amount = rate of growth/decay = number of time periods = $1000 Amt. after t time periods 5% 6 = 0.05

20. Holt Geometry 3-1 Lines and Angles A(t) = a(1 + r) t A(6) = 1000(1 + 0.05) 6 A(6) = 1000(1.05) 6 A(6) ≈ $1340.095641 The account contains $1340.10 after 6 years.

21. Holt Geometry 3-1 Lines and Angles SummarySummarize/reflect D What did I do? L What did I learn? I What did I find most interesting? Q What questions do I still have? What do I need clarified?

22. Holt Geometry 3-1 Lines and Angles  Notes 7.1  Graphing Calc.

23. Holt Geometry 3-1 Lines and Angles 4. Suppose you invest $500 in a savings account that pays 3.5% annually. How much will be in the account after 5 years?

24. Holt Geometry 3-1 Lines and Angles A(t) = a = r = t = A(t) = a(1 + r) t $500 Amt. after t time periods 3.5% 5 = 0.035

25. Holt Geometry 3-1 Lines and Angles A(t) = a(1 + r) t A(5) = 500(1 + 0.035) 5 A(5) = 500(1.035) 5 A(5) ≈ $593.8431528 The account contains $593.84 after 5 years.

26. Holt Geometry 3-1 Lines and Angles 5. Suppose you invest $1000 in a savings account that pays 5% annually.

27. Holt Geometry 3-1 Lines and Angles If you make no additional deposits or withdrawals, how many years will it take for the account to grow to at least $1500?

28. Holt Geometry 3-1 Lines and Angles A(t) = a = r = t = A(t) = a(1 + r) t $1000 Amt. after t time periods 5% ? = 0.05

29. Holt Geometry 3-1 Lines and Angles A(t) = a(1 + r) t A(t) = 1000(1 + 0.05) t A(t) = 1000(1.05) t Use the table on the calculator.

30. Holt Geometry 3-1 Lines and Angles The account will contain $1500 after 9 yrs.

31. Holt Geometry 3-1 Lines and Angles 6. Suppose you invest $500 in a savings account that pays 3.5% annually. When will the account contain $650?

32. Holt Geometry 3-1 Lines and Angles A(t) = a(1 + r) t A(t) = 500(1 + 0.035) t A(t) = 500(1.035) t Use the table on the calculator.

33. Holt Geometry 3-1 Lines and Angles The account will contain $650 after 8 years.

34. Holt Geometry 3-1 Lines and Angles SummarySummarize/reflect D What did I do? L What did I learn? I What did I find most interesting? Q What questions do I still have? What do I need clarified?

35. Holt Geometry 3-1 Lines and Angles 7.1: Math XL Start Notes 7.2 Work on the Study Plan

36. Holt Geometry 3-1 Lines and Angles TOPIC: 7.2 Properties of Exponential Functions Name: Daisy Basset Date : Period: Subject: Notes Objective: Graph exponential functions showing intercepts and end behavior.

37. Holt Geometry 3-1 Lines and Angles Key Concept  Parent Function  Stretch, Shrink, Reflection