Let's idealize a single bacterium as a sphere with radius R. The bacterium lives in a lake and needs oxygen to survive. There is oxygen dissolved in the lake water with concentration cO. But the oxygen nearby gets depleted, as the bacterium uses it up. The lake is huge, so the bacterium won't affect its overall oxygen level; instead, the environment near the bacterium will come to a quasi-steady state, in which the oxygen concentration doesn't depend on time. In this state, the oxygen concentration c(r) will depend on the distance r from the center of the bacterium. Very far away, we know c(∞) = cO. We'll assume that every oxygen molecule that reaches the bacterium's surface gets immediately gobbled up. Hence, at the surface c(R) = 0. A. Find the full concentration profile c(). Hint: Because we're in quasi-steady state, oxygen does not pile up anywhere: The number of molecules per time crossing each shell equals the number per time crossing the next shell.