A biologist starts an experiment with a culture containing 40{,}000 bacteria. During an initial growth phase, the population increases by...

1. TRANSLATE the problem information

• Given information:
  • Initial bacteria population: 40,000
  • Population increases by 150% during growth phase
  • Chemical then eliminates 98% of current population
• What this tells us: We need to apply these percentage changes sequentially

2. INFER the approach

• This is a two-step problem where each percentage change applies to the current population
• First calculate the population after growth, then apply the elimination to that grown population
• Key insight: The 98% elimination applies to the 100,000 bacteria (after growth), not the original 40,000

3. SIMPLIFY the growth calculation

• "Increases by 150%" means the new amount = original + 150% of original
• This equals \(\mathrm{100\% + 150\% = 250\%}\) of the original = \(\mathrm{2.5}\) times the original
• Population after growth = \(\mathrm{40{,}000 \times 2.5 = 100{,}000}\) bacteria

4. SIMPLIFY the elimination calculation

• "Eliminates 98%" means 98% are removed, so \(\mathrm{100\% - 98\% = 2\%}\) remain
• Convert 2% to decimal: \(\mathrm{2\% = 0.02}\)
• Remaining bacteria = \(\mathrm{100{,}000 \times 0.02 = 2{,}000}\) bacteria

Answer: C) 2,000

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Misinterpreting "increases by 150%" to mean the population becomes 150% of the original (instead of 250% of the original).

Students often think "increases by 150%" means "becomes 150% of original," leading them to calculate \(\mathrm{40{,}000 \times 1.5 = 60{,}000}\) for the grown population. Then applying 2% remaining: \(\mathrm{60{,}000 \times 0.02 = 1{,}200}\). Since 1,200 isn't an answer choice, this leads to confusion and guessing.

Second Most Common Error:

Poor INFER reasoning: Applying the 98% elimination to the original population instead of the grown population.

Students correctly calculate the grown population as 100,000, but then mistakenly think the chemical eliminates 98% of the original 40,000 bacteria. This gives: \(\mathrm{40{,}000 \times 0.98 = 39{,}200}\) eliminated, leaving \(\mathrm{100{,}000 - 39{,}200 = 60{,}800}\). Since this isn't close to any answer choice, this leads to abandoning systematic solution and guessing.

The Bottom Line:

This problem requires careful attention to the sequence of operations and precise interpretation of percentage language. The key insight is recognizing that each step operates on the current population, not the original population.