Differential Equations Exam Review (3 of 6) - Review 2 L8-L14 1 A tank holds 10,000 L and contains initially 10 kg of salt Pure water enters the tank at

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

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1 Review 2: L8-L14 1. A tank holds 10,000 L and contains initially 10 kg of salt. Pure water enters the tank at a constant rate of 5 L/min. The solution is kept well stirred and flows out at the same rate of 5 L/min. (a) Find the amount of salt in the tank at a time t(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/L begins to enter the tank at a rate of 5 L/min. The solution is kept well stirred and flows out 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, that is, t→ ∞3. A tank contains 10,000 L of pure water. A solution with salt concentration 0.2 kg/L begins to enter the tank at a rate of 5 L/min. The solution is kept well stirred and flows out at a rate of 3 L/min. (a) Write a differential equation that models the rate of change of ( )x t, where ( )x tis the amount 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 limiting concentration 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 as 1200. (a) Write a differential equation for the rate of change according to the model described above (exponential (or Malthusian) model). . is ?

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