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Welcome To. Scientific Notation. Exponential Growth and Decay. Properties of exponents. Exponents. Geometry Sequences. $100. $100. $100. $100. $100. $200. $200. $200. $200. $200. $300. $300. $300. $300. $300. $400. $400. $400. $400. $400. $500. $500. $500. $500. $500.

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Welcome To

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  1. Welcome To

  2. Scientific Notation Exponential Growth and Decay Properties of exponents Exponents Geometry Sequences $100 $100 $100 $100 $100 $200 $200 $200 $200 $200 $300 $300 $300 $300 $300 $400 $400 $400 $400 $400 $500 $500 $500 $500 $500

  3. Exponents for $100 Simplify: 4-3

  4. Answer 4-3 = 1/43 = 1/64 Back

  5. Exponentsfor $200 Simplify: (0.023454)0

  6. Answer (0.023454)0 = 1 Back

  7. Exponents for $300 Simplify: 3-2 * 40

  8. Answer 3-2 * 40 = 1/32 * 1 = 1/9 Back

  9. Exponents for $400 Simplify: 22/(3*2)-2

  10. Answer 22/(3*2)-2 = 4*(3*2)2 = 4* 62 = 4*36 = 144 Back

  11. Exponentsfor $500 Evaluate (2x3)/(3-2y-5) for x = -2 and y = 4

  12. Answer (2x3)/(3-2y-5) for x = -2 and y = 4 =2x3*32y5 = 2*9 *x3y5 = 18x3y5 = 18(-2)3(4)5 = 18*-8*1024 = -147456 Back

  13. Scientific Notationfor $100 Write the following number in scientific Notation: 3,450,000

  14. Answer 3,450,000 = 3.45 x 106 Back

  15. Scientific Notationfor $200 Write the following number in scientific Notation: .000073

  16. Answer .000073 = 7.3 x 10-5 Back

  17. Scientific Notationfor $300 Simplify. Write your answer in scientific notation: (3.24 x 10-4)(5.2 x 10-2)

  18. Answer (3.24 x 10-4)(5.2 x 10-2) = 3.24*5.2 x 10-4 * 10-2 = 16.848 x 10-6 = 1.6848 x 10-5 Back

  19. Scientific Notationfor $400 Simplify. Write your answer in scientific notation: (7.1 x 10-2)(2.3 x 104)

  20. Answer (7.1 x 10-2)(2.3 x 104) = 7.1*2.3 x 10-2 * 104 = 16.33 x 102 = 1.633 x 103 Back

  21. Scientific Notationfor $500 Simplify. Write your answer in scientific notation: ((1.3 x 103)(9.1 x 1012))2

  22. Answer ((1.3 x 103)(9.1 x 1012))2 (1.32 x 106)(9.12 x 1024) = (1.3*9.1)2 x 106 * 1024 = 139.9489 x 1030 = 1.399489 x 1032 Back

  23. Properties of Exponentsfor $100 Simplify: 2x-1 * 3x5

  24. Answer 2x-1 * 3x5 = 2*3*x-1+5 = 6x4 Back

  25. Properties of Exponentsfor $200 Simplify: (3x-3)/(9x4)

  26. Answer (3x-3)/(9x4) = (3/9)*x-3 – 4 = (1/3)x-7 = 1/(3x7) Back

  27. Properties of Exponentsfor $300 Simplify: (x-3x5)/(x2y0)

  28. Answer (x-3x5)/(x2y0) = (x-3+5)/(x2*1) = x2/x2 = 1 Back

  29. Properties of Exponentsfor $400 Simplify: (y-7y3)-1

  30. Answer (y-7y3)-1 = (y-7+3)-1 = (y-4)-1 = y4 Back

  31. Properties of Exponentsfor $500 Simplify: (9x-2y5)2 * (3y2x-1)-3

  32. Answer (9x-2y5)2 * (3y2x-1)-3 = (92x-2*2y5*2)2 * (3-3y2*-3x-1*-3)-3 = (81x-4y10) * ((1/27)y-6x3) = (81/27)(x-4x3)(y10y-6) = (3y4)/x Back

  33. Geometric Sequencesfor $100 Find the next three terms in the following geometric sequence: 3, 9, 27, 81, …

  34. Answer The common ratio is 3, so the next three terms are: 81*3 = 243 243*3 = 729 729*3 = 2187 243, 729, 2187 Back

  35. Geometric Sequencesfor $200 Write the formula for finding the nth term of a geometric sequence

  36. A(n) = a1 * (r)n-1 Where: n is the nth term a1 is the first term r is the common ratio Answer Back

  37. Geometric Sequencesfor $300 Find the 8th, 11th, and 13th terms in the following geometric sequence: A(n) = 4(3)n-1

  38. Answer A(n) = 4(3)n-1 A(8) = 4(3)8-1 = 4(3)7 = 8,748 A(11) = 4(3)11-1 = 4(3)10 = 236,196 A(13) = 4(3)13-1 = 4(3)12 = 2,125,764 Back

  39. Geometric Sequencesfor $400 Is the following sequence geometric, arithmetic, or neither? WHY? 4, 8, 12, 16, ….,

  40. Answer The sequence is arithmetic because the next term is found by adding 4 to the previous term. A geometric sequence would progress by multiplying, not adding. Back

  41. Geometric Sequencesfor $500 What is the difference between the equation for geometric sequences and the equation for exponential growth or decay?

  42. Answer The equation for a geometric sequence is to the power of n-1, while exponential growth and decay is to the power of x, not x-1. Geometric sequence: A(n) = a1 * (r)n-1 Exponential growth/decay: y = a * (b)x Back

  43. Exponential Growth and Decayfor $100 Is the following equation exponential growth or exponential decay? Why? A(n) = 5*(0.4)n

  44. Answer Exponential decay because r = 0.4 which means 0<r<1, thus telling you that it is exponential decay Back

  45. Exponential Growth and Decayfor $200 Is the following equation exponential growth or exponential decay? Why? A(n) = 0.2*(7)n

  46. Answer Exponential growth because r = 7 which means r>1, thus telling you that it is exponential growth Back

  47. Exponential Growth and Decayfor $300 Write an equation to model the following situation (in other words, write an equation to find the number of balls left after n days) Josh started with 200 balls, but loses half of them every day

  48. Answer A(n) = 200(0.5)n Back

  49. Exponential Growth and Decayfor $400 Joe invested $3200 in an account that earned 4% interest compounded every 3 months. Find the account balance after 5 years.

  50. Answer y = a*bx where y = final balance, a = initial amount, b = interest rate and x = the number of times the interest is compounded. So, a = 3200, b = 4% = 1 + .04 = 1.04 and x = 20 (4 per year for 5 years) y = 3200(1.04)20 = $7011.59 Back

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