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Bacteria Growth worksheet

Grades 10–12 · CCSS HSF.LE.A.4, HSF.LE.A.1.c

Solve each problem and show your work. Round answers to 2 decimal places where needed.

1.
Problem 1.
- Solve for: Time
- Time unit: Minutes
- Starting count (N₀): 1,400
- Final count (N): 70,000
- Doubling time (g): 18
Find: Time needed (t)
Answer
2.
Problem 2.
- Solve for: Final count
- Time unit: Minutes
- Starting count (N₀): 800
- Elapsed time (t): 80
- Doubling time (g): 21
Find: Final count (N)
Answer
3.
Problem 3.
- Solve for: Time
- Time unit: Hours
- Starting count (N₀): 1,050
- Final count (N): 75,000
- Doubling time (g): 16
Find: Time needed (t)
Answer
4.
Problem 4.
- Solve for: Final count
- Time unit: Days
- Starting count (N₀): 820
- Elapsed time (t): 130
- Doubling time (g): 20
Find: Final count (N)
Answer
5.
Problem 5.
- Solve for: Doubling time
- Time unit: Days
- Starting count (N₀): 1,400
- Final count (N): 55,000
- Elapsed time (t): 160
Find: Doubling time (g)
Answer
6.
Problem 6.
- Solve for: Final count
- Time unit: Days
- Starting count (N₀): 1,225
- Elapsed time (t): 95
- Doubling time (g): 22
Find: Final count (N)
Answer
7.
Problem 7.
- Solve for: Doubling time
- Time unit: Days
- Starting count (N₀): 750
- Final count (N): 55,000
- Elapsed time (t): 84
Find: Doubling time (g)
Answer
8.
Problem 8.
- Solve for: Final count
- Time unit: Days
- Starting count (N₀): 950
- Elapsed time (t): 110
- Doubling time (g): 23
Find: Final count (N)
Answer
9.
Problem 9.
- Solve for: Final count
- Time unit: Days
- Starting count (N₀): 1,175
- Elapsed time (t): 140
- Doubling time (g): 13
Find: Final count (N)
Answer
10.
Problem 10.
- Solve for: Time
- Time unit: Minutes
- Starting count (N₀): 1,200
- Final count (N): 65,000
- Doubling time (g): 15
Find: Time needed (t)
Answer

Answer key: Bacteria Growth worksheet

1. Time needed (t): 101.59 minutes
1. Count the doublings needed to grow from the start to the final count (log base 2 of the growth)
  $log₂ (\frac{70,000}{1,400})$ $= 5.643856$
2. Multiply the doublings by the doubling time to get the time needed
  $t$ $= 18 min \times 5.643856$ $= 101.589411 min$
3. Divide ln 2 by the doubling time to get the growth rate at any moment
  $\frac{ln 2}{18 min}$ $= 0.03850818 per min$
2. Final count (N): 11,216.85
1. Count the generations: divide the time by the doubling time
  $\frac{80 min}{21 min}$ $= 3.809524$
2. Each generation doubles the count, so multiply the start by 2 once per generation
  $800 \times 2^{3.809524}$ $= 11,216.850275$
3. Divide ln 2 by the doubling time to get the growth rate at any moment
  $\frac{ln 2}{21 min}$ $= 0.03300701 per min$
3. Time needed (t): 98.53 hours
1. Count the doublings needed to grow from the start to the final count (log base 2 of the growth)
  $log₂ (\frac{75,000}{1,050})$ $= 6.158429$
2. Multiply the doublings by the doubling time to get the time needed
  $t$ $= 16 h \times 6.158429$ $= 98.53487 h$
3. Divide ln 2 by the doubling time to get the growth rate at any moment
  $\frac{ln 2}{16 h}$ $= 0.0433217 per h$
4. Final count (N): 74,217.93
1. Count the generations: divide the time by the doubling time
  $\frac{130 d}{20 d}$ $= 6.5$
2. Each generation doubles the count, so multiply the start by 2 once per generation
  $820 \times 2^{6.5}$ $= 74,217.927753$
3. Divide ln 2 by the doubling time to get the growth rate at any moment
  $\frac{ln 2}{20 d}$ $= 0.03465736 per d$
5. Doubling time (g): 30.21 days
1. Count how many doublings it took to grow from the start to the final count (log base 2)
  $log₂ (\frac{55,000}{1,400})$ $= 5.295933$
2. Divide the time by the number of doublings to get the time for one
  $g$ $= \frac{160 d}{5.295933}$ $= 30.211863 d$
3. Divide ln 2 by the doubling time to get the growth rate at any moment
  $\frac{ln 2}{30.211863 d}$ $= 0.02294288 per d$
6. Final count (N): 24,436.46
1. Count the generations: divide the time by the doubling time
  $\frac{95 d}{22 d}$ $= 4.318182$
2. Each generation doubles the count, so multiply the start by 2 once per generation
  $1,225 \times 2^{4.318182}$ $= 24,436.462862$
3. Divide ln 2 by the doubling time to get the growth rate at any moment
  $\frac{ln 2}{22 d}$ $= 0.03150669 per d$
7. Doubling time (g): 13.56 days
1. Count how many doublings it took to grow from the start to the final count (log base 2)
  $log₂ (\frac{55,000}{750})$ $= 6.196397$
2. Divide the time by the number of doublings to get the time for one
  $g$ $= \frac{84 d}{6.196397}$ $= 13.556265 d$
3. Divide ln 2 by the doubling time to get the growth rate at any moment
  $\frac{ln 2}{13.556265 d}$ $= 0.05113113 per d$
8. Final count (N): 26,147.63
1. Count the generations: divide the time by the doubling time
  $\frac{110 d}{23 d}$ $= 4.782609$
2. Each generation doubles the count, so multiply the start by 2 once per generation
  $950 \times 2^{4.782609}$ $= 26,147.626948$
3. Divide ln 2 by the doubling time to get the growth rate at any moment
  $\frac{ln 2}{23 d}$ $= 0.03013683 per d$
9. Final count (N): 2,050,686.91
1. Count the generations: divide the time by the doubling time
  $\frac{140 d}{13 d}$ $= 10.769231$
2. Each generation doubles the count, so multiply the start by 2 once per generation
  $1,175 \times 2^{10.769231}$ $= 2,050,686.905966$
3. Divide ln 2 by the doubling time to get the growth rate at any moment
  $\frac{ln 2}{13 d}$ $= 0.05331901 per d$
10. Time needed (t): 86.39 minutes
1. Count the doublings needed to grow from the start to the final count (log base 2 of the growth)
  $log₂ (\frac{65,000}{1,200})$ $= 5.759333$
2. Multiply the doublings by the doubling time to get the time needed
  $t$ $= 15 min \times 5.759333$ $= 86.390001 min$
3. Divide ln 2 by the doubling time to get the growth rate at any moment
  $\frac{ln 2}{15 min}$ $= 0.04620981 per min$