A laboratory sample initially has a mass of 120 grams at time t = 0 days. Each day thereafter, the...

1. TRANSLATE the problem information

• Given information:
  • Initial mass: 120 grams at time \(\mathrm{t = 0}\) days
  • Mass change: loses exactly 5 grams each day
  • Rate: constant sublimation rate

• What this tells us: The mass decreases by the same fixed amount every day.

2. INFER the mathematical relationship

• Key insight: "Loses exactly 5 grams each day" means the rate of change is constant
• Constant rate of change = \(\mathrm{-5}\) grams per day
• Mathematical functions with constant rates of change are linear functions
• The function form: \(\mathrm{M(t) = 120 - 5t}\)

3. INFER the function characteristics

• Since the slope \(\mathrm{(-5)}\) is negative, this is a decreasing function
• This gives us a decreasing linear function
• Exponential functions would involve constant percentage changes (like "loses 10% of remaining mass each day"), not constant absolute amounts

Answer: B (Decreasing linear)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students confuse constant absolute change with constant percentage change and think "constant rate" automatically means exponential function.

They might reason: "The problem mentions a constant rate, and I remember exponential functions involve rates, so this must be exponential." They fail to distinguish between constant absolute change (linear) versus constant percentage change (exponential).

This may lead them to select Choice A (Decreasing exponential).

Second Most Common Error:

Inadequate TRANSLATE reasoning: Students misinterpret "loses exactly 5 grams each day" and think the amount lost increases over time.

They might think: "As time goes on, more mass is lost because the process continues," failing to recognize that "exactly 5 grams each day" means the same amount every single day.

This leads to confusion and guessing among the choices.

The Bottom Line:

The key challenge is distinguishing between constant absolute change (which creates linear functions) and constant percentage change (which creates exponential functions). Students must carefully analyze what type of "constant rate" the problem describes.