A fish tank initially contains 15 liters of pure water. Brine of constant, but unknown, concentration of salt is flowing in at 4 liters per

Question

A fish tank initially contains 15 liters of pure water. Brine of constant, but unknown, concentration of salt is flowing in at 4 liters per minute. The solution is mixed well and drained at 4 liters per minute. Let xx be the amount of salt, in grams, in the fish tank after tt minutes have elapsed. Find a formula for the rate of change in the amount of salt, dx/dtdx/dt, in terms of the amount of salt in the solution xx and the unknown concentration of incoming brine cc. dxdt

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Hải Đăng 4 years 2021-09-05T00:52:55+00:00 1 Answers 130 views 0

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  1. thaiduong
    0
    2021-09-05T00:54:04+00:00
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    Answer:

    dx/dt = 4c – 4x/15

    Step-by-step explanation:

    a. Find a formula for the rate of change in the amount of salt, dx/dtdx/dt, in terms of the amount of salt in the solution

    Let c be the concentration of the incoming brine in grams per liter. Since it flows in at a rate of 4 liters per minute, the mass flow in is thus 4m.

    Let x be the mass of salt present at time, t. The concentration of salt present at time, t is thus mass of salt/volume of tank = x/15. Since the well mixed solution is drained at 4 liters per minute, the mass flow out is thus 4x/15.

    The net rate of change of amount of salt dx/dt = mass flow in – mass flow out

    dx/dt = 4c – 4x/15

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