A 85-gallon tank initially holds 30 gallons of salt water containing 6 pounds of salt. Suppose salt water containing 5 pounds of salt per gallon is pumped into the top of the tank at the rate of 8 gallons per minute, while a well-mixed solution leaves the bottom of the tank at a rate of 4 gallons per minute. Let S(t) represent the number of pounds of salt in the vat after tt minutes. (A) Write the DE model for the time rate of change of salt in the vat. Also include the initial condition. dS/dt= S(0)= (B) Solve the initial value problem to find the amount of salt in the vat as a function of time. S(t)= (C) How much salt is in the tank when the tank is full?
Differential Equation
A 85-gallon tank initially holds 30 gallons of salt water containing 6 pounds of salt. Suppose salt water containing 5 pounds of salt per gallon is pumped into the top of the tank at the rate of 8 gallons per minute, while a well-mixed solution leaves the bottom of the tank at a rate of 4 gallons per minute.
Let S(t) represent the number of pounds of salt in the vat after tt minutes.
(A) Write the DE model for the time rate of change of salt in the vat. Also include the initial condition.
dS/dt=
S(0)=
(B) Solve the initial value problem to find the amount of salt in the vat as a function of time.
S(t)=
(C) How much salt is in the tank when the tank is full?
pounds
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