The dye dilution method is used to measure cardiac output wi

The dye dilution method is used to measure cardiac output with 5 mg of dye. The dye concentrations, in mg/L, are modeled by c(t) = 28te^-0.8t, 0 lessthanorequalto t lessthanorequalto 10, where t is measured in seconds. Find the cardiac output. 43.619 L/s

Solution

amount of dye ,A=5 mg

_{[0 to 10]}c(t) dt

=_{[0 to 10]}(28te^-0.8t) dt

=28_{[0 to 10]}(te^-0.8t) dt

=28[_{[0 to 10]}(-1_/0.8)te^-0.8t-_{[0 to 10]}(-1_/0.8)e^-0.8tdt ]

=28[_{[0 to 10]}(-1_/0.8)te^-0.8t-(1_/0.8²)e^-0.8t ]

=28[[(-1_/0.8)*10e^-0.8*10-(1_/0.8²)e^-0.8*10]-[(-1_/0.8)*0*e^-0.8*0-(1_/0.8²)e^-0.8*0]]

=43.6179

cardiac output =A/_{[0 to 10]}c(t) dt

cardiac output =5_/43.6179

cardiac output =0.1146 L/s