A municipal water treatment facility utilizes 3 identical backup filtration units to process stormwater runoff. The average volume of water, , in thousands of gallons, remaining to be filtered per unit hours after the units are activated is modeled by the equation:
where . Which of the following is the best interpretation of the number in this context?
- AThe initial total volume of water, in thousands of gallons, remaining to be filtered by all 3 units combined.
- BThe rate, in thousands of gallons per hour, at which water is filtered by each individual unit, which is 4.8.
- The rate, in thousands of gallons per hour, at which water is filtered by all 3 units combined.Answer
- DThe rate, in thousands of gallons per hour, at which water is filtered by each individual unit, which is 4.6.
Answer
The rate, in thousands of gallons per hour, at which water is filtered by all 3 units combined.
The correct answer is the option stating that 14.4 represents the rate, in thousands of gallons per hour, at which water is filtered by all 3 units combined. In the given equation , we can isolate the total volume remaining, , as . In this form, the rate of change of the total volume is , indicating that the combined remaining volume decreases by 14.4 thousand gallons each hour.
Step-by-Step Solution
Key Concept
Interpreting coefficients and constants in a linear relationship within a real-world context, particularly when variables represent averages or totals.