Question
A 10,000-gallon swimming pool needs to be emptied. Exactly 2,000 gallons have already been pumped out of the pool and into the tanker. As the pump is pumping water, the amount of water in the pool decreases at a constant rate of 720 gallons per hour.
Which number represents the y-intercept? The slope? Write an equation to represent the situation. Then, graph the function.
Enter your answer.
Convince Me! How is the rate of change of this function different from that in Example 1? Explain.
Enter your answer.
A place to graph the function describing the amount of water in the pool over time.
Which number represents the y-intercept? The slope? Write an equation to represent the situation. Then, graph the function.
Enter your answer.
Convince Me! How is the rate of change of this function different from that in Example 1? Explain.
Enter your answer.
A place to graph the function describing the amount of water in the pool over time.
Answers
GPT-5 mini
Let t = time in hours since now, and y = gallons of water remaining in the pool.
- y-intercept: 8000 (since 10,000 − 2,000 = 8,000 gallons are in the pool at t = 0)
- slope: −720 (gallons per hour; the pool is losing 720 gallons each hour)
Equation:
y = 8000 − 720t
Graphing notes:
- Plot (0, 8000) as the y-intercept.
- Another point: after 1 hour, y = 8000 − 720 = 7,280 → (1, 7280).
- x-intercept (when pool is empty): set y = 0 → t = 8000/720 ≈ 11.11 hours. The line through these points with slope −720 gives the graph.
Convince Me:
The rate of change here is −720 gallons/hour, a negative rate meaning the quantity is decreasing over time. In Example 1 the rate of change was positive (the quantity was increasing), so the sign of the slope is different — here the slope points downward (loss of water) rather than upward (gain).
- y-intercept: 8000 (since 10,000 − 2,000 = 8,000 gallons are in the pool at t = 0)
- slope: −720 (gallons per hour; the pool is losing 720 gallons each hour)
Equation:
y = 8000 − 720t
Graphing notes:
- Plot (0, 8000) as the y-intercept.
- Another point: after 1 hour, y = 8000 − 720 = 7,280 → (1, 7280).
- x-intercept (when pool is empty): set y = 0 → t = 8000/720 ≈ 11.11 hours. The line through these points with slope −720 gives the graph.
Convince Me:
The rate of change here is −720 gallons/hour, a negative rate meaning the quantity is decreasing over time. In Example 1 the rate of change was positive (the quantity was increasing), so the sign of the slope is different — here the slope points downward (loss of water) rather than upward (gain).