$\"\"$

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The flow rate of a water at a pumping station is

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$\"\"$ .

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Where $\"\"$ is flow rate of water in thousands of gallons per hourand $\"\"$ is

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time in hours.

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The value of $\"\"$ lies between $\"\"$ .

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(a) Use a graphing utility to graph the rate function and approxiamate the

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maximum flow rate at the pumping station.

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Graph the function: $\"\"$ .

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$\"\"$ .

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Observe the graph:

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The maximum flow rate at the pumping station is $\"\"$ at $\"\"$ .

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$\"\"$

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(b) Approxiamate the total volume of water pumped in one day.

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The flow rate of a water at a pumping station is,

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$\"\"$ .

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The total volume of water pumped in one day is $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ $\"\"$ thousand gallons.

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The total volume of water pumped in one day is $\"\"$ thousand gallons.

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$\"\"$

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(a) Graph of the function $\"\"$ is

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$\"\"$ .

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The maximum flow rate at the pumping station is $\"\"$ at $\"\"$ .

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(b) The total volume of water pumped in one day is $\"\"$ thousand gallons.