A pharmaceutical company is developing a spherical coating to encase a medicine. As a first attempt at a mathematical model, they assume that the volumetric rate at which this coating dissolves will be proportional to its surface area, kS=k(4r2). The medicine within the coating will be modeled as a sphere of radius 1.00mm, and the coating itself will be 0.75mm thick, resulting in a sphere that is 3.50mm in diameter. It is desired for the coating to take 20.0 minutes to dissolve in acid, to simulate how it will behave in the stomach. For this to work, they need to know the constant of proportionality k that the coating material must exhibit, and then they will find a material with this property. You have been asked to help them with this task. (The volume of a sphere is V=34r3.) Please make sure in addressing this prompt that you do the following: - Clearly depict and explain an appropriate choice of system. - Derive the time-dependent mass balance equation that describes this process. You will need to clearly define additional variables or parameters not listed above. Please communicate the units of every number and variable. - Show the work necessary to get to the "variable-separated" part of your mathematical model, so that you can clearly communicate the bounds on your definite integrals. - Show the work necessary from there to obtain the expression for the proportionality constant, then numerically evaluate this expression, reporting both a number and its units as your final result