1. [CLO 1 and 2;30 points; Simple mathematical model development and solving |" order ODE] A 500L cylindrical tank is initially filled with 200L of pure water. Compound A then flows into the tank with a concentration of 10g/L at a volumetric flow rate of 5L/ minute, in which compound A will be converted to compound B following first-order kinetics with a reaction constant of 0.1/ minute. If at the same time the tank outlet is also opened with a volumetric flow rate of 5L/min, and assume that the density of the solution is similar at various concentratior.s of compounds A and B and the mixing in the tank occurs homogeneously, a. Construct a mathematical model that describes the change in the concentration of compound A in the tank as a function of time. b. Determine the concentration of compound A in the tank 1 hour after compound A was added to the tank c. Determine the concentration of compound A in the tank at a steady state. d. If after a steady state there is damage to the outflow shells so that the outflow of the tank stops, determine the concentration of compound A in the tank exactly when the tank is full. Fist oraes mohic