Consider a homogeneous spherical aggregate of bacteria of radius r. Species A diffuses into the bacteria, and the concentration of species A at the surface of the bacteria, cAr, is known. (a) Write all assumptions to derive a mathematical model. ( 1 point) (b) Determine independent and dependent variables. ( I point) (c) Develop a mathematical equation describing the concentration of species A through the bacteria aggregation at steady-state condition. (3 points) (d) Determine the initial and/or boundary conditions to solve the derived mathematical model. (2 points) (e) Solve the model equation using these conditions which you chose in part (d). (3 points)