Solve the following problems, showing any necessary work. 1. [1 point] Sugar wat

Question

Solve the following problems, showing any necessary work. 1. [1 point] Sugar water is diluted at the Aloc-Acoc Beverage Company to provide a variety of quantities of sugar in their drunks. The process uses a tank, which begins filled with 3000 L of pure water. Sugar water with a concentration of 1500 g/L is pumped into this tank at a rate of 25 L/minute. The solution is mixed, and is pumped out at a rate of 20 L/minute. Letting S(t) denote the amount of sugar in the tank at time t, set up BUT DO NOT SOLVE an initial value problem that describes the function S(t).

Explanation / Answer

rate of change of sugar=rate of inflow -rate of outflow

s'(t)=1500*25 - 20*(s(t))/(3000+(25-20)t)

s'(t)=37500 - 20(s(t))/(3000+5t)

s(0) =0 as there is no salt

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