BellRinger 1/30/2012. Compare and contrast: Linear functions. Quadratic functions. Polynomial functions. Exponential functions

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1 BellRinger 1/30/2012 Compare and contrast: Linear functions Quadratic functions Polynomial functions Exponential functions

3 BellRinger 1/31/2012 Write a formula for each sequence: a) 6, 9, 12, 15, b) 6, 12, 24, 48, c) 6, -6, -18, -30,

4 Whiteboard Problems from Yesterday s WKST: Unit 7 Activity 1 3. Demone, Catrice, Chris 4. Lindsey, Janiqua, Markell 5. George, Patrice, Dexter 3. Alonzo, Mary, Kyren 4. Willie, Yonisha, Regina, Devon 5. Ciara, Ja Corian, Eryn

6 BellRinger- 2/1/2012 Write the first four terms of each sequence. t n = 3 + 5n t n = 4(3) n t n = 2n 2

7 Today Recursive series & sequences t 0 = 5 t n = 3(t n-1 ) + 2

8 Recursive Series & Sequences t 0 = 1 t n = 4(t n-1 ) Write the formula for the sequence.

9 Recursive Series & Sequences Write a recursive series: 5, 10, 15, 20,

10 Recursive Series & Sequences Write a recursive series: 5, 10, 20, 40,

11 Recursive Series & Sequences Write a recursive series: 12, 6, 3, 1½, Write the formula for a series:

13 BellRinger 2/2/2012 Write the recursive equation and the n-th term equation for the series. 10, -20, 40, -80, 160, -320

14 Fibonacci Sequence The Fibonacci sequence is one of the most famous sequences. t 1 = 1 t 2 = 1 t n = t n-1 + t n-2 Write the first 8 terms of the sequence:

15 Using a calculator for sequences

16 Practice Write the first five terms of the sequence

17 Practice Write the first five terms of the sequence

18 Practice Write the first five terms of the sequence

19 Practice Write the first five terms of the sequence

20 Practice Write a recursive formula:

21 Practice Egor has two parents, four grandparents, and so on. Write an explicit formula and a recursive formula for the number of ancestors Egor has if we go back n generations.

22 Practice The sum of the interior angles of a triangle is 180º, of a quadrilateral is 360º and of a pentagon is 540º. Assuming this pattern continues, find the sum of the interior angles of a dodecagon (12 sides).

23 Practice After knee surgery, your trainer tells you to return to your jogging program slowly. He suggests jogging for 12 minutes each day for the first week. Each week thereafter, he suggests that you increase that time by 6 minutes per day. How many weeks will it be before you are up to jogging 60 minutes per day?

25 BellRinger 2/3/2012 A culture of bacteria doubles every 2 hours. If there are 500 bacteria at the beginning, how many bacteria will there be after 24 hours?

27 BellRinger 2/6/2012 Sue has a credit card balance of $3500. She plans to pay $100 per month. Her card charges 1% per month on any unpaid balance. How many months will it take her to pay off? How much will she end up paying?

28 BellRinger 2/6/2012 Sue has a credit card balance of $3500. She plans to pay $100 per month. Her card charges 1% per month on any unpaid balance. How many months will it take her to pay off?

29 BellRinger 2/6/2012 Sue has a credit card balance of $3500. She plans to pay $100 per month. Her card charges 1% per month on any unpaid balance. How much will she end up paying?

30 Quiz Folder Quiz

31 Finite Series Find the sum of the first 10 terms of the sequence: 4, 8, 12, 16,

32 Finite series Find the sum of the first 25 terms of:

34 BellRinger 2/7/2012 Write an equation for the sequence: 10, 16, 22, 28, Find the sum of the first 100 terms of the sequence.

35 Assignment Fix the numbers so you can answer the question #3 - Its profits for the last 4 years have been $32 million, $38 million, $44 million, and $50 million. If Any questions?

37 Arithmetic Series The sum of the first n terms of an arithmetic series are: S n = n( t + t ) 1 n 2 or, if n starts at zero S n 1 n( t + t 1) = 0 n 2

38 Arithmetic Series

39 Arithmetic Series

40 Geometric Series For t n = a r n-1 * Use n-1 so that the first term is a, second is a r, third is a r 2 The sum of the first n terms of a geometric series: S n n a(1 r ) = 1 r

41 Geometric series S n n a(1 r ) = 1 r Find the sum of the first 10 terms of the geometric series

42 Finite series Find the sum of the first 20 terms of the geometric series t n = 5 3 n

43 Finite series Find the sum of the first 20 terms of the geometric series t n = n

44 Finite series The cost of groceries for a family of four is $280 per month. The price of groceries is going up by 0.3% each month. How much would the family expect to pay for groceries over the next three years?

45 Unit 7 Activity 3 This must be turned in! One note on #5 a house depreciates by 1 / 40 of its original value each year. Everyone do Problem #2 we ll discuss in a few minutes.

47 BellRinger 2/8/2012 Find the sum of the first 20 terms of the geometric series: 8, 12, 18, 27,

48 Unit 7 Activity 3

50 BellRinger 2/9/2012 An auditorium has 20 seats on the first row, 23 seats on the second row, 26 seats on the third row, and so on. It has 25 rows of seats. How many seats are in the auditorium?

51 Schedule Today Convergent and divergent series Tomorrow Limits Monday Review series & sequences Tuesday Six-Weeks exam sequences & series

52 Series Convergent series gets closer and closer to a fixed value ( asymptote ) Divergent series does not converge to an asymptote Goes to infinity or infinity or is periodic

53 Convergent Series Divergent Series

55 BellRinger 2/10/2012 Determine whether each sequence converges, and to what value. n tn 1 = t =10 5n n

56 Convergence - Limits The limit is the value that a function or sequence approaches as the input approaches some value. lim3 n n

57 Convergence - Limits The limit is the value that a function or sequence approaches as the input approaches some value. 1 lim n n

58 Convergence - Limits The limit is the value that a function or sequence approaches as the input approaches some value. 3 lim n 1+ n

59 Convergence - Limits The limit is the value that a function or sequence approaches as the input approaches some value. n ( 4 2n) lim +

60 Unit7 Act. 4 1 Markell, Lindsey, George 2 Mary, Catrice, Regina 3 Patrice, Janiqua, Ciara 4 Kyren, Ja Corian, Dexter 5 Willie, AJ, Chris, Yonisha 6 Demone, Devon, Eryn

62 BellRinger- 2/13/2012 Evaluate the limit: lim x ( ) 2 x 2

63 Today: Evaluate limits of expressions Use sequences and series to solve problems

64 Unit7 Act. 4 1 Markell, Lindsey, George 2 Mary, Catrice, Regina 3 Patrice, Janiqua, Ciara 4 Kyren, Ja Corian, Dexter 5 Willie, AJ, Chris, Yonisha 6 Demone, Devon, Eryn

65 Review

66 BellRinger- 2/14/2012 Write an equation for the sequence 8, 20, 50, 125,

67 Test Sequences & Series

A sequence is an ordered list of numbers. Each number in a sequence is called a term. a 1, a 2, a 3,..., a n

A sequence is an ordered list of numbers. Each number in a sequence is called a term. a 1, a 2, a 3,..., a n Algebra 2/Trig Unit 8 Sequences and Series Lesson 1 I can identify a pattern found in a sequence. I can use a formula to find the nth term of a sequence. I can write a recursive formula for a sequence.