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Zorluk: ZorInterpreting Linear Relationships in Context

During a dry season, the volume of water VV, in millions of gallons, in a municipal reservoir dd days after the start of a monitoring period is modeled by the equation V=248−1.8dV = 248 - 1.8d, where 0≤d≤600 \leq d \leq 60. According to the model, at what rate, in gallons per minute, is water leaving the reservoir?

Cevap: 1250 gallons per minute

Cevap

The reservoir is losing water at a rate of 1,2501,250 gallons per minute.
The slope of the linear equation V=248−1.8dV = 248 - 1.8d is −1.8-1.8, indicating a decrease of 1.81.8 million gallons of water per day. To express this rate in gallons per minute, we perform the unit conversion. First, convert 1.81.8 million gallons to gallons: 1.8×1,000,000=1,800,0001.8 \times 1,000,000 = 1,800,000 gallons. Second, convert 11 day to minutes: 24 hours/day×60 minutes/hour=1,44024 \text{ hours/day} \times 60 \text{ minutes/hour} = 1,440 minutes. Finally, divide the total gallons by the total minutes: 1,800,000 gallons1,440 minutes=1,250\frac{1,800,000 \text{ gallons}}{1,440 \text{ minutes}} = 1,250 gallons per minute.

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1
Identify the daily rate of water leaving the reservoir from the given linear equation.
The daily rate is 1.81.8 million gallons per day.
The slope of the linear equation V=248−1.8dV = 248 - 1.8d is −1.8-1.8, which represents the rate of change of the volume with respect to time in days. The negative sign indicates a decrease, meaning water is leaving at a rate of 1.81.8 million gallons per day.
2
Convert the volume from million gallons to gallons.
1,800,0001,800,000 gallons.
To convert from millions of gallons to gallons, multiply the value by 1,000,0001,000,000, resulting in 1.8×1,000,000=1,800,0001.8 \times 1,000,000 = 1,800,000.
3
Convert the time unit from days to minutes.
1,4401,440 minutes.
There are 2424 hours in a day and 6060 minutes in an hour, so 1 day=24×60=1,440 minutes1 \text{ day} = 24 \times 60 = 1,440 \text{ minutes}.
4
Calculate the rate in gallons per minute.
1,2501,250 gallons per minute.
Divide the volume in gallons by the time in minutes: 1,800,000 gallons1,440 minutes=1,250\frac{1,800,000 \text{ gallons}}{1,440 \text{ minutes}} = 1,250.

Anahtar Kavram

Interpreting the slope of a linear relationship in context and performing unit conversions on rates.
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Konular

Interpreting Linear Relationships in Context

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