question archive The rate at which a contaminant leaves a storm sewer and enters a lake depends on two factors: the concentration of the contaminant in the water from the sewer and the rate at which the water leaves the sewer

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The rate at which a contaminant leaves a storm sewer and enters a lake depends on two factors: the concentration of the contaminant in the water from the sewer and the rate at which the water leaves the sewer. Both of these factors vary with time. The concentration of the contaminant, in kilograms per cubic metre of water, is given by c(t) = t2 , where t is in seconds. The rate at which water leaves the sewer, in cubic metres per second, is given by w(t)=1t4+10. Determine the time at which the contaminant leaves the sewer and enters the lake at the maximum rate.