A tank initially contains s0 lb of salt dissolved in 200 gallons of water, where s0 is a non-negative number. Starting at time t = 0 measured in minutes, water containing 0.5lb of salt per gallon enters the tank at a rate of 4 gal/min, and the well-stirred solution leaves the tank at the same rate.
(a) Describe the situation using a differential equation, let x represent the amount of salt in the tank at a given time t.
(b) Classify the differential equation.
(c) Find x(t) a function describing the amount of salt in the tank at time t. Include units in your final answer.
(d) Find c(t) a function describing the concentration of salt in the tank at time t. Include units in your final answer.
(e) Find the limiting values for x(t) and c(t) as t -> infinity. Explain the meaning of these limits (use complete sentences to create the description).