Question:The function \(\mathrm{V(t) = 620 - 15t}\) gives the estimated volume, in liters, of water remaining in a tank t...

1. TRANSLATE the function components

• Given: \(\mathrm{V(t) = 620 - 15t}\) represents volume remaining after t minutes
• The function has two parts:
  • Constant term: 620
  • Variable term: \(\mathrm{-15t}\)

2. INFER what \(\mathrm{t = 0}\) represents

• Since t is "minutes after the valve is opened"
• At \(\mathrm{t = 0}\), the valve has just been opened (starting moment)
• This is when we want to know what 620 represents

3. SIMPLIFY by evaluating \(\mathrm{V(0)}\)

• \(\mathrm{V(0) = 620 - 15(0)}\)
• \(\mathrm{V(0) = 620 - 0 = 620}\)
• So when the valve first opens, there are 620 liters in the tank

4. TRANSLATE back to context

• The constant 620 represents the initial volume when timing begins
• This matches choice (C): "The tank is estimated to contain 620 liters of water when the valve is opened"

Answer: C

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students see the large number 620 and assume it must represent the "most important" quantity - often confusing it with the drainage rate.

They might think "620 must be how fast it drains because it's the biggest number," leading them to select Choice A (620 liters per minute). However, the drainage rate is actually the coefficient -15, meaning 15 liters per minute out.

Second Most Common Error:

Poor INFER reasoning about time reference: Students don't recognize that \(\mathrm{t = 0}\) is the key moment to examine. Instead, they might substitute \(\mathrm{t = 1}\) to see what happens "after some time."

When they calculate \(\mathrm{V(1) = 620 - 15(1) = 605}\), they get confused about which number (620 or 605) the question is asking about, potentially leading to Choice E (after 1 minute, about 620 liters remain).

The Bottom Line:

Linear functions in real-world contexts require careful attention to what each parameter represents. The constant term always tells you the starting value when the input variable equals zero - in this case, the volume when \(\mathrm{t = 0}\) (valve just opened).