The function \(\mathrm{w(t) = 300 - 4t}\) models the volume of liquid, in milliliters, in a container t seconds after...

1. TRANSLATE the problem information

• Given information:
  • \(\mathrm{w(t) = 300 - 4t}\) models volume in milliliters
  • \(\mathrm{t}\) represents seconds after draining begins
  • Question asks: "volume draining from the container each second"
• What this tells us: We need the rate at which volume changes per unit time.

2. INFER the mathematical approach

• "Volume draining each second" means rate of change of volume with respect to time
• In a linear function, the coefficient of the variable gives us this rate
• We need to identify the slope of this linear function

3. INFER the rate from the function structure

• Rewrite \(\mathrm{w(t) = 300 - 4t}\) as \(\mathrm{w(t) = -4t + 300}\)
• This is in the form \(\mathrm{y = mx + b}\) where:
  • \(\mathrm{m = -4}\) (slope/rate of change)
  • \(\mathrm{b = 300}\) (initial volume when \(\mathrm{t = 0}\))
• The slope \(\mathrm{-4}\) means volume decreases by 4 milliliters each second
• Therefore, 4 milliliters drain each second

Answer: D. 4

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students may misinterpret "volume draining each second" as asking for the volume remaining rather than the rate of change. They might focus on calculating \(\mathrm{w(1) = 300 - 4(1) = 296}\), thinking this represents the drainage rate.

This may lead them to select Choice B (296).

Second Most Common Error:

Poor INFER reasoning: Students recognize they need a rate but confuse which part of the function represents it. They might think the initial value (300) represents the drainage rate since it's the largest number, or misunderstand that the negative slope indicates the direction of change but the magnitude (4) is what drains.

This may lead them to select Choice A (300).

The Bottom Line:

This problem tests whether students can distinguish between a function's output value and its rate of change. The key insight is recognizing that "per unit time" language signals we need the slope, not a function evaluation.