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Exponential growth and decay

Year 13 maths · Fieldbook Learning

Name ______________________ Date __________

Count the doublings or half-lives, then multiply or divide by 2 that many times.

  1. A bacteria culture starts with 30 cells and doubles every 6 hours. How many cells are there after 36 hours?
  2. A 400 mg sample has a half-life of 5 days. How much is left after 20 days?
  3. A 180 mg sample has a half-life of 3 days. How much is left after 6 days?
  4. A 2,560 mg sample has a half-life of 7 days. How much is left after 42 days?
  5. A bacteria culture starts with 120 cells and doubles every 3 hours. How many cells are there after 12 hours?
  6. A bacteria culture starts with 110 cells and doubles every 4 hours. How many cells are there after 8 hours?
  7. A 140 mg sample has a half-life of 3 days. How much is left after 6 days?
  8. A bacteria culture starts with 120 cells and doubles every 8 hours. How many cells are there after 40 hours?
  9. A bacteria culture starts with 20 cells and doubles every 6 hours. How many cells are there after 36 hours?
  10. A 960 mg sample has a half-life of 3 days. How much is left after 12 days?
  11. A bacteria culture starts with 300 cells and doubles every 8 hours. How many cells are there after 16 hours?
  12. A 3,200 mg sample has a half-life of 6 days. How much is left after 36 days?
  13. A 560 mg sample has a half-life of 4 days. How much is left after 16 days?
  14. A 640 mg sample has a half-life of 8 days. How much is left after 32 days?
  15. A bacteria culture starts with 10 cells and doubles every 7 hours. How many cells are there after 42 hours?
  16. A bacteria culture starts with 230 cells and doubles every 4 hours. How many cells are there after 8 hours?
  17. A 20 mg sample has a half-life of 4 days. How much is left after 8 days?
  18. A 640 mg sample has a half-life of 7 days. How much is left after 35 days?
  19. A 960 mg sample has a half-life of 6 days. How much is left after 36 days?
  20. A bacteria culture starts with 280 cells and doubles every 7 hours. How many cells are there after 14 hours?
More free practice: fieldbooklearning.com/uk/practice/year-13/exponential-growth-and-decay/

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Answer key: Exponential growth and decay

  1. 1,920
  2. 25 mg
  3. 45 mg
  4. 40 mg
  5. 1,920
  6. 440
  7. 35 mg
  8. 3,840
  9. 1,280
  10. 60 mg
  11. 1,200
  12. 50 mg
  13. 35 mg
  14. 40 mg
  15. 640
  16. 920
  17. 5 mg
  18. 20 mg
  19. 15 mg
  20. 1,120