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  1. 1Solving 4x−7=2x+9
  2. 2Linear cost equation
  3. 3System of two equations
  4. 4No solution, linear system
  5. 5Infinite solutions, linear system
  6. 6Weight limit word problem
  7. 7Solving a linear inequality
  8. 8Rate of change, cost per hour
  9. 9Finding slope then extending line
  10. 10Percent increase then decrease
  11. 11Percent: part is 18% of what
  12. 12Ratio split of 66 members
  13. 13Converting mph to ft/s
  14. 14Printer rate word problem
  15. 15Probability from a table
  16. 16Fraction from a table
  17. 17Mean shift, finding new value
  18. 18Median from a frequency table
  19. 19Factoring a quadratic
  20. 20Sum of roots, quadratic
  21. 21Vertex form of a parabola
  22. 22One solution, discriminant=0
  23. 23Max height of a parabola
  24. 24Percent growth rate, 1.03^t
  25. 25Exponential decay, 15% off
  26. 26Exponential growth, doubling
  27. 27Evaluating f(−2)
  28. 28Finding a, then g(-2)
  29. 29Composing f and g
  30. 30Shifting a graph f(x−3)+1
  31. 31Circle by completing the square
  32. 32Radius from two points
  33. 33Arc length from central angle
  34. 34Complementary angles in a triangle
  35. 35Tangent in a right triangle
  36. 36Isosceles right triangle area
  37. 37Similar triangles ratio
  38. 38Volume of a cylinder
  39. 39Volume of a sphere
  40. 40Scaling a box's volume
  41. 41Supplementary angles equation
  42. 42Setting up a cost equation
  43. 43Slope between two points
  44. 44x-intercept of a line
  45. 45Slope of perpendicular line
  46. 46Solving a linear system
  47. 47Two-ticket system of equations
  48. 48Solving a fraction equation
  49. 49Solving 7-3x>2x-18
  50. 50Height when planted, w=0
  51. 51No solution, linear equation
  52. 52Taxi cost inequality
  53. 53Intersecting lines, find k
  54. 54System of two equations
  55. 55Scaling 9x-6y+5
  56. 56Costly text message inequality
  57. 57Product of roots
  58. 58Matching exponent bases
  59. 59Solving a square root equation
  60. 60Equation with same denominator
  61. 61Vertex of a parabola
  62. 62Factor theorem on a cubic
  63. 63Exponential decay, halving
  64. 64Percent growth per year
  65. 65Solving f(a)=21 for a quadratic
  66. 66x²+y² from sum and product
  67. 67Sum of roots of intersection
  68. 68Exponential growth, V=2500(1.04)^t
  69. 69Composing g(x)=f(x+2)-3
  70. 70Completing the square
  71. 71Price per ounce comparison
  72. 72Percent increase
  73. 73Percent off, then tax
  74. 74Mean with a score removed
  75. 75Overlapping sets, neither
  76. 76Map scale ratio problem
  77. 77Converting rate units
  78. 78Line of best fit
  79. 79Median of a data set
  80. 80Scaling up a sample
  81. 81Percent of a percent
  82. 82Average speed, unequal times
  83. 83Ratio of flour to sugar
  84. 84Two successive percent decreases
  85. 85Fraction of a subgroup
  86. 86Mixing to a target percent
  87. 87Triangle angle sum
  88. 88Ladder as right triangle
  89. 89Area of a trapezoid
  90. 9030-60-90 triangle sides
  91. 91Area of a circle sector
  92. 92Inscribed angle theorem
  93. 93Circle from diameter endpoints
  94. 94Volume of a cone
  95. 95Cube volume to surface area
  96. 96Sine-cosine complementary angles
  97. 97Area ratio of similar triangles
  98. 98Diagonal of a rectangle
  99. 99Same-side interior angles
  100. 100Right triangle, tan from cos
  101. 101Volume displaced raises water

63Exponential decay, halving

A sample of a radioactive substance has a mass of 640 grams. Its mass is halved every 6 days. What is the mass of the sample, in grams, after 30 days?

After 30 days the sample has 20 grams left. 30 days means 5 half-life periods, so M = 640(1/2)⁵ = 640/32 = 20 g; halving step by step (640→320→160→80→40→20) confirms it.

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