The pressure exerted on a scuba diver at sea level is 14.70 pounds per square inch (psi). For each foot...

1. TRANSLATE the problem information

• Given information:
  • Pressure at sea level: \(14.70\text{ psi}\)
  • Pressure increases by \(0.44\text{ psi}\) for each foot below sea level
  • Need total pressure at \(105\text{ feet}\) below sea level

• What this tells us: We have a starting value (14.70) that increases at a constant rate (0.44 per foot)

2. TRANSLATE the relationship into mathematical form

• The total pressure follows the pattern: Starting pressure + (Rate × Depth)
• Total pressure = \(14.70 + (0.44 \times \text{depth in feet})\)
• For 105 feet: Total pressure = \(14.70 + (0.44 \times 105)\)

3. SIMPLIFY the calculation

• First calculate the additional pressure: \(0.44 \times 105 = 46.2\text{ psi}\) (use calculator)
• Then add to the base pressure: \(14.70 + 46.2 = 60.90\text{ psi}\)

Answer: A. 60.90

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students might only calculate the additional pressure from depth (\(0.44 \times 105 = 46.2\)) and forget to add the initial sea-level pressure of \(14.70\text{ psi}\).

This incomplete reasoning leads them to think the answer should be around \(46\text{ psi}\), but since that's not an option, they might select Choice B (31.50) as the closest value, or become confused and guess.

Second Most Common Error:

Poor TRANSLATE reasoning: Students might misunderstand what "total pressure" means and think they only need the pressure at sea level, ignoring the depth entirely.

This leads them to select Choice C (14.70) - the sea-level pressure without considering the additional pressure from being underwater.

The Bottom Line:

This problem tests whether students can properly set up a linear relationship from a real-world context. The key insight is recognizing that "total pressure" means the base pressure PLUS the additional pressure from depth, not just one or the other.