A storage tank contains fuel and is drained at a constant rate after a pump is turned on.The amount of...

1. TRANSLATE the question

• We need to interpret the t-intercept of \(\mathrm{F(t) = 60 - 5t}\)
• The t-intercept is where the graph crosses the t-axis (horizontal axis)
• This occurs when the function value \(\mathrm{F(t)}\) equals zero

2. INFER what to find

• To find the t-intercept, set \(\mathrm{F(t) = 0}\)
• This will tell us when the fuel amount reaches zero (tank becomes empty)

3. SIMPLIFY to solve for t

• Set up: \(\mathrm{60 - 5t = 0}\)
• Add 5t to both sides: \(\mathrm{60 = 5t}\)
• Divide by 5: \(\mathrm{t = 12}\)

4. TRANSLATE the mathematical result back to context

• \(\mathrm{t = 12}\) means after 12 hours
• \(\mathrm{F(t) = 0}\) means zero liters of fuel remaining
• Therefore: The tank is empty after 12 hours

Answer: B

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students confuse different parts of linear functions

Many students mix up intercepts, thinking the t-intercept describes what happens at \(\mathrm{t = 0}\). They see "intercept" and immediately think about the starting value (60 liters), leading them to select Choice A (At time t = 0, there are 60 liters of fuel in the tank).

Second Most Common Error:

Poor INFER reasoning: Students recognize they need the slope but misinterpret the context

Students correctly identify that the coefficient -5 represents the rate of change but don't properly interpret the t-intercept concept. They focus on the rate information and select Choice C (For each additional hour, the amount of fuel decreases by 5 liters).

The Bottom Line:

Success requires distinguishing between different features of linear functions (intercepts vs. slope) and accurately translating mathematical concepts into real-world interpretations. The t-intercept specifically tells you when the dependent variable reaches zero.