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Dye Dilution Is a Method of Measuring Cardiac Output AmgA \mathrm { mg }

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Dye dilution is a method of measuring cardiac output. If AmgA \mathrm { mg } of dye is used and c(t)c ( t ) is the concentration of the dye at time tt , then the cardiac output over the time interval [0,T][ 0 , T ] is given by
F=A0Tc(t)dtF = \frac { A } { \int _ { 0 } ^ { T } c ( t ) d t }
Find the cardiac output over the time interval [0,15][ 0,15 ] if the dye dilution method is used with 11mg11 \mathrm { mg } of dye and the dye concentration, in mg/L\mathrm { mg } / \mathrm { L } , is modeled by
c(t)=12t(15t),0t15c ( t ) = \frac { 1 } { 2 } t ( 15 - t ) , 0 \leq t \leq 15
where tt is measured in seconds.

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