3. $100 $200 $300 $400 $500 $200 $300 $400 $500 Exponents Scientific Notation Exponential Growth and Decay Properties of exponents Geometry Sequences

4. Exponents for $100 Simplify: 4 -3

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

6. Exponents for $200 Simplify: (0.023454) 0

7. Answer Back (0.023454) 0 = 1

8. Exponents for $300 Simplify: 3 -2 * 4 0

9. Answer 3 -2 * 4 0 = 1/3 2 * 1 = 1/9 Back

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

11. Answer Back 2 2 /(3*2) -2 = 4*(3*2) 2 = 4* 6 2 = 4*36 = 144

12. Exponents for $500 Evaluate (2x 3 )/(3 -2 y -5 ) for x = -2 and y = 4

13. Answer (2x 3 )/(3 -2 y -5 ) for x = -2 and y = 4 =2x 3 *3 2 y 5 = 2*9 *x 3 y 5 = 18x 3 y 5 = 18(-2) 3 (4) 5 = 18*-8*1024 = -147456 Back

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

15. 3,450,000 = 3.45 x 10 6 Answer Back

16. Scientific Notation for $200 Write the following number in scientific Notation:.000073

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

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

19. 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

20. Scientific Notation for $400 Simplify. Write your answer in scientific notation: (7.1 x 10 -2 )(2.3 x 10 4 )

21. = 7.1*2.3 x 10 -2 * 10 4 = 16.33 x 10 2 = 1.633 x 10 3 Answer Back

22. Scientific Notation for $500 Simplify. Write your answer in scientific notation: ((1.3 x 10 3 )(9.1 x 10 12 )) 2

23. Answer ((1.3 x 10 3 )(9.1 x 10 12 )) 2 (1.3 2 x 10 6 )(9.1 2 x 10 24 ) = (1.3*9.1) 2 x 10 6 * 10 24 = 139.9489 x 10 30 = 1.399489 x 10 32 Back

24. Properties of Exponents for $100 Simplify: 2x -1 * 3x 5

25. Answer 2x -1 * 3x 5 = 2*3*x -1+5 = 6x 4 Back

26. Properties of Exponents for $200 Simplify: (3x -3 )/(9x 4 )

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

28. Properties of Exponents for $300 Simplify: (x -3 x 5) /(x 2 y 0 )

29. = (x -3+5 )/(x 2 *1) = x 2 /x 2 = 1 Answer Back

30. Properties of Exponents for $400 Simplify: (y -7 y 3 ) -1

31. Answer (y -7 y 3 ) -1 = (y -7+3 ) -1 = (y -4 ) -1 = y 4 Back

32. Properties of Exponents for $500 Simplify: (9x -2 y 5 ) 2 * (3y 2 x -1 ) -3

33. Answer (9x -2 y 5 ) 2 * (3y 2 x -1 ) -3 = (9 2 x -2*2 y 5*2 ) 2 * (3 -3 y 2*-3 x -1*-3 ) -3 = (81x -4 y 10 ) * ((1/27)y -6 x 3 ) = (81/27)(x -4 x 3 )(y 10 y -6 ) = (3y 4 )/x Back

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

35. 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

36. Geometric Sequences for $200 Write the formula for finding the nth term of a geometric sequence

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

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

39. 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

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

41. 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

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

43. 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) = a 1 * (r) n-1 Exponential growth/decay: y = a * (b) x Back

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

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

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

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

48. Exponential Growth and Decay for $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

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

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

51. Answer Back y = a*b x 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

52. Exponential Growth and Decay for $500 Graph the following equation without using a calculator: y = 3 *(1/2) x

53. Answer Back XY 6 03 13/2 23/4