1. A tank initially contains 90lbs of salt dissolved in 20 gal of water. Brine containing 2 lb/gal of
salt flows into
the tank at the rate of 3 gal/min, and the mixture flows out of the tank at the same rate.
a.) Set up the ODE that represents the rate of change of the salt with respect to time.
b.) Find the general solution to the ODE. (Hint: You can use separation of variables of
integrating
factors.)
c.) Use the method from Objective 1.1 to verify that the solution you found in part (b) really is a
solution to the ODE.
d.) Find the particular solution to the ODE (using the initial condition stated in the problem).
e.) How much salt does the tank contain after 6 minutes?
f.) Use the Slope Field Tool to sketch the vector field and compare it to your answer for part (e).
2. A tank originally contains 100 gallons of fresh water, but can hold up to 300 gallons. Water
containing 1/2lb of salt per gallon is poured into the tank at a rate of 4 gal/min, and the mixture
is allowed to leave at a rate of 1 gal/min. How much salt is in the tank at time t? What is the
domain of the function?

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