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r-ruslan [8.4K]
3 years ago
14

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?
Mathematics
1 answer:
astraxan [27]3 years ago
3 0
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 liters

Answer: 613.135 liters



 

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