A tank contains 300 liters of fluid in which 40 grams of salt is dissolved. Brine containing 1 gram of salt per liter is then pumped into th

Question

A tank contains 300 liters of fluid in which 40 grams of salt is dissolved. Brine containing 1 gram of salt per liter is then pumped into the tank at a rate of 6 L/min; the well-mixed solution is pumped out at the same rate. Find the number A(t) of grams of salt in the tank at time t.

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Ariana 2 weeks 2021-09-12T06:02:06+00:00 2 Answers 0

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    0
    2021-09-12T06:03:19+00:00

    Answer:

    A(t) = 300 -260e^(-t/50)

    Step-by-step explanation:

    The rate of change of A(t) is …

    A'(t) = 6 -6/300·A(t)

    Rewriting, we have …

    A'(t) +(1/50)A(t) = 6

    This has solution …

    A(t) = p + qe^-(t/50)

    We need to find the values of p and q. Using the differential equation, we ahve …

    A'(t) = -q/50e^-(t/50) = 6 – (p +qe^-(t/50))/50

    0 = 6 -p/50

    p = 300

    From the initial condition, …

    A(0) = 300 +q = 40

    q = -260

    So, the complete solution is …

    A(t) = 300 -260e^(-t/50)

    ___

    The salt in the tank increases in exponentially decaying fashion from 40 grams to 300 grams with a time constant of 50 minutes.

    0
    2021-09-12T06:03:39+00:00

    Answer:

    Thx that awnser rlllly helped

    Step-by-step explanation:

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