Modeling Nutrient Diffusion into a Prokaryotic Cell (20 pts, 4+2+5+5+4) Consider a prokaryotic cell fully submerged in a nutrient bath. The initial concentration of nutrients in the bath is ( = 0) = . Lets model the diffusion of nutrients into the cell as a semi-infinite source of diffusing nutrients.A. Draw a concentration profile that represents this system.

A. Draw a concentration profile that represents this system. You should label the position axis (x), the concentration axis ( , the initial concentration level , and the portions of ) the profile that represent the bath and the cell itself. B. What kind of function should you use for this problem and why? C. Propose an expression (, ) to model this system. Is your solution a general solution of Ficks second law? D. Write out the two time boundary conditions and two spatial boundary conditions below for this system and show that your solution satisfies them. Time: ( > 0, ) & ( > 0, = 0) Space: (, > 0) & ( 0, > 0) Hint: (0) = 0, () = 1, ( ) = 1. E. Sketch (, ) for several time steps including to identify important concentration evolution with time.