A tank with a maximum capacity for 50 liters originally contains 5 liters of wat

Question

A tank with a maximum capacity for 50 liters originally contains 5 liters of water with 15 grams of salt in solution. Fresh water is poured in the tank at a rate or 3 liters per minute. The stirred water is allowed to pour out the tank at a rate of 2 liters per minute. a. Find the function V volume of water in the tank. In liters. V(t) = 1 + 5 b. Find the time t_c when the tank is about to overflow. t_c = 45 c. Find the differential equation satisfied by the function Q, the total amount of salt in the tank measured in grams. Q'(t) =

Explanation / Answer

a)volume of water in tank

V(t)=5 +t(3-2)

V(t)=5 +t

b)when tank is about to over flow ,volume of water =50 L

5+t =50

t =45 min

c)rate of salt inflow =0

rate of salt out flow =2*Q/(5+t)

rate of change of amount of salt =rate of inflow -rate of out flow

Q'(t)=0 -2Q/(5+t)

Q'(t)=-2Q/(5+t) where Q(0)=15

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