Hello, i need help with this exercise, i need every step of tge procedure explained. REQUIRED POLYMATH

Controlled drug release is important for the treatment of several diseases. Figure 1 shows an experimental device inserted under the skin and in contact with the tissue for the release of a drug (F). The device consists of a container containing the drug in capsules which dissolve over time in a physiological solution. The lateral surface of the container is provided with a permeable membrane which allows the drug to be released into the surrounding tissue. The exchange surface (A) of the membrane is 6 cm. The drug outside the membrane of the device is consumed instantly. The drug transport coefficient across the membrane is 1.3*10^-6 cm/sec.

This is Figure 1, the schematic representation of drug delivery device.

The drug capsules dissolve in the physiological solution with a release rate expressed by the following relationship:

where Cf is the drug concentration in the liquid phase, Rs0 (3.5 mg/hr) the solubilization rate, and k (0.2 mL^2/(mg*hr)) a constant. The volume (Vt) which contains the physiological solution and the drug capsules is equal to 4 cm while the volumetric fraction occupied by the capsules is equal to 30%.

a) Determine the concentration of the drug in the liquid phase in contact with the capsules and the flow of the drug released by the device under steady state conditions;

b) Use polymath to determine the time profile of the drug (Cf) in liquid phase in contact with the capsules assuming that the volume of the capsules does not vary over time. What is the time required to reach 50% of the concentration determined in point a)?

Required polymath

rs=rs0k1Cf2