A community swimming pool with a 7{,}800-gallon capacity is being drained for maintenance. Due to the drainage system, water flows...

1. TRANSLATE the problem information

• Given information:
  • Pool capacity: 7,800 gallons
  • Drainage rate: 325 gallons per hour (constant rate)
  • Need to determine function type for remaining water vs time

2. INFER the mathematical relationship

• The key phrase is "constant rate" - this tells us the amount changes by the same value each time period
• After 1 hour: \(\mathrm{7,800 - 325 = 7,475}\) gallons remaining
• After 2 hours: \(\mathrm{7,800 - 650 = 7,150}\) gallons remaining
• After t hours: \(\mathrm{7,800 - 325t}\) gallons remaining

3. INFER the function type from the pattern

• The equation \(\mathrm{W(t) = 7,800 - 325t}\) has the form \(\mathrm{y = mx + b}\)
• This is a linear function because the rate of change is constant (\(\mathrm{-325}\) gallons per hour)
• The slope is negative because water is flowing OUT, so the amount decreases

4. INFER the direction

• Since the slope (\(\mathrm{-325}\)) is negative, the function is decreasing
• Each hour, there are 325 fewer gallons than the previous hour

Answer: (B) Decreasing linear

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Not recognizing that "constant rate" automatically indicates a linear function

Students may overthink the draining process and assume it should be exponential because "things empty out faster when there's more water." This misconception leads them away from the crucial detail that the problem explicitly states a constant rate of 325 gallons per hour.

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

Second Most Common Error:

Poor INFER reasoning: Correctly identifying linear but getting the direction wrong

Students might focus on the mathematical relationship without carefully considering the physical context. They see "rate of 325 gallons per hour" but miss that it's flowing OUT of the pool, leading them to think the amount is increasing.

This may lead them to select Choice (D) (Increasing linear)

The Bottom Line:

The phrase "constant rate" is the definitive clue for linear functions. Students who miss this connection often get distracted by the draining context and overthink the problem, when the mathematical relationship is actually straightforward.