2. A tank is initially filled with 100 L of salt solution with a concentration of 0.12 kg/L. At time t = 0, a solution containing 0.2 kg/L of salt is poured into the tank at a rate of 3 L/min. Simultaneously, a drain is opened in the bottom of the tank allowing the solution to leave the tank at a rate of 4 L/min. The tank is well-stirred. Let x(t) represent the amount of salt (in kg) in the tank after t minutes. Find the differential equation and initial condition for which r(t) is a solution. DO NOT SOLVE THE DIFFERENTIAL EQUATION. t)= x' (t) = , x(0) =

A grafted durian tree is growing at the rate of H'(t) =÷+ metres per 5 2t +1 (t+1)² year, where i is time in years. (i) Given that the durian tree is already 1 meter tall when grafted (i.e. t = 0 ), find an expression for H(t), the height of the durian tree.

A brine solution of salt flows at a constant rate of 8 L/min into a large tank that initially held 100 L of brine solution in which was dissolved 0.2 kg of salt. The solution inside the tank is kept well stirred and flows out of the tank at the same rate. If the concentration of salt in the brine entering the tank is 0.04 kg/L, determine the mass of salt in the tank after t min. When will the concentration of salt in the tank reach 0.01 kg/L? Determine the mass of salt in the tank after t min. mass 4-4e 2t 25 kg