4) Nutrient diffusion into tissue ( 9 pts) Consider a homogeneous slab of tissue of thickness L that is able to consume nutrient A that diffuses into it with a first-order reaction with molar rate RA=k1CA. (a) Suppose the slab of tissue is bounded on each side by a well-mixed concentration of A equal to CA0. Derive an expression for the steady-state concentration of A within the slab. From this expression, derive an appropriate expression for the flux NA at the surface of the slab ( r=R). (b) Now consider as the starting point that the slab initially (at time 0 ) has a uniform concentration CAO and that the surroundings have zero concentration with the above first order reaction occurring. Derive an infinite series expression for the time-dependent concentration profile in the slab