Differential Equations Exam Review (3 of 6) - Review 2:...

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1Review 2: L8-L141. A tank holds 10,000 L and contains initially 10 kg of salt. Pure water enters the tank ata constant rate of 5 L/min. The solution is kept well stirred and flows out at the same rateof 5 L/min.(a) Find the amount of salt in the tank at a timet(b) What is the limiting amount of salt in the tank as time increases indefinitely?2. A tank contains 10,000 L of pure water. A solution with salt concentration 0.2 kg/Lbegins to enter the tank at a rate of 5 L/min. The solution is kept well stirred and flowsout at the same rate of 5 L/min.(a) Write the initial value problem that models the rate of change of( )x t, where( )x tthe amount of salt in the tank at a time t.(b) Find the amount of salt in the tank at a time t.(c) What is the amount of salt in the tank in 1 hour?(d) Find the concentration of salt( )C tat a time t.(e) When will the concentration of salt in the tank reach 0.002 kg/L?(f) What is the limiting concentration of salt in the tank as time increases indefinitely, thatis,t→ ∞3. A tank contains 10,000 L of pure water. A solution with salt concentration 0.2 kg/Lbegins to enter the tank at a rate of 5 L/min. The solution is kept well stirred and flowsout at a rate of 3 L/min.(a) Write a differential equation that models the rate of change of( )x t, where( )x tis theamount of salt in the tank at a time t.(b) Find the amount of salt in the tank at a time t.(c) Find the concentration of salt( )C tat a time t.(d) Assuming that the tank can hold very large amount of solution, find the limitingconcentration of salt in the tank as time increases indefinitely?4. A certain population changes at a rate proportional to the size of the population.Initially there were 1000 animals. In 3 years the number of animals was measured as1200.(a) Write a differential equation for the rate of change according to the model describedabove (exponential (or Malthusian) model)..is?

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