Water is pumped out of a holding tank at a rate of 6-6e^-0.13t liters/minute, where t is in minutes since the pump is started. I f the holding tank contains 1000 liters of water when the pump is started, how much water does it hold one hour later?
1 answer:
Procedure : 1) Integrate the function, from t =0 to t = 60 minutues to obtain the number of liters pumped out in the entire interval, and 2) Substract the result from the initial content of the tank (1000 liters).Hands on : Integral of (6 - 6e^-0.13t) dt ]from t =0 to t = 60 min = = 6t + 6 e^-0.13t / 0.13 = 6t + 46.1538 e^-0.13t ] from t =0 to t = 60 min = 6*60 + 46.1538 e^(-0.13*60) - 0 - 46.1538 = 360 + 0.01891 - 46.1538 = 313.865 liters 2) 1000 liters - 313.865 liters = 613.135 litersAnswer: 613.135 liters
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