A medication has an initial concentration of 96 mg in a patient's bloodstream. Every 6 hours, the patient's body eliminates...

1. TRANSLATE the elimination information

• Given information:
  • Initial concentration: \(\mathrm{96\ mg}\)
  • Every 6 hours: \(\mathrm{70\%}\) is eliminated
  • Find concentration after 12 hours

• What this tells us: If \(\mathrm{70\%}\) is eliminated, then \(\mathrm{30\%}\) (or \(\mathrm{0.3}\)) remains after each 6-hour period

2. INFER the time structure

• We need to go from 0 hours to 12 hours
• Since elimination happens every 6 hours, this means we have two 6-hour periods
• We'll need to apply the \(\mathrm{30\%}\) retention factor twice in sequence

3. SIMPLIFY through sequential calculations

• After first 6 hours: \(\mathrm{96 \times 0.3 = 28.8\ mg}\)
• After second 6 hours (total 12 hours): \(\mathrm{28.8 \times 0.3 = 8.64\ mg}\) (use calculator)

Answer: B (\(\mathrm{8.64\ mg}\))

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misinterpret "\(\mathrm{70\%}\) eliminated" as "\(\mathrm{70\%}\) remains" instead of recognizing that \(\mathrm{30\%}\) remains.

Using \(\mathrm{70\%}\) retention:

\(\mathrm{96 \times 0.7 = 67.2}\)

\(\mathrm{67.2 \times 0.7 = 47.04}\)

This leads them to select Choice D (\(\mathrm{47.04\ mg}\)) or Choice E (\(\mathrm{67.2\ mg}\)) if they only apply the factor once.

Second Most Common Error:

Poor INFER reasoning: Students recognize that \(\mathrm{30\%}\) remains but only apply the reduction once, thinking 12 hours means one application instead of recognizing two sequential 6-hour periods.

Stopping after one application: \(\mathrm{96 \times 0.3 = 28.8}\)

This may lead them to select Choice C (\(\mathrm{28.8\ mg}\))

The Bottom Line:

This problem tests whether students can correctly interpret complementary percentages (eliminated vs. remaining) and recognize that sequential time periods require sequential applications of the same process. The mathematical calculations are straightforward once the setup is correct.