Bacterial foraging Bacteria use swimming to seek out food. Imagine the bacterium is in a region of low food concentration. For the bacterium to profit from swimming to a region with more food it needs to reach the food-rich region before diffusion makes the concentrations in the two regions the same. Here we find the smallest distance that a bacterium needs to swim to outrun diffusion. a) Make a plot in which you sketch the distance traveled by a bacterium swimming at a constant velocity v as a function of time, and the distance over which a food molecule will diffuse in that time. Indicate on the plot the smallest time and the smallest distance that the bacterium needs to swim to outrun diffusion. b) Make a numerical estimate of these minimum times and distances for an E. coli swimming at a speed of 30μm/s. The diffusion constant for a typical food molecule is D 500μm 2 /s. c) Estimate the number of ATP molecules the bacterium must hydrolyze per second in order to travel at this speed, assuming all the energy goes into overcoming fluid drag. Note that the energy release from one ATP molecule is ∼20k B T. You can assume a spherical bacterium of radius ∼1μm.