A cylindrical fiber is represented by the core- conductor model. The upstroke of the trans- membrane potential is given by a template function as Vm(x) = 50 tanh(x) (x in mm). The fiber's radius is a, and the intracellular and extracellular resistances are r; and re. (Note that r; and re are in "unit length" form.) Vm is understood to be the spatial distribution of Vm at one moment during propagation of an action potential. At this time, which is after propagation began, there are no stimuli. Give the mathematical expression for the answer, and plot normalized wave shapes, (wave shapes having peaks scaled to 1), for each part below. a. Plot Vm (x) from z of 4 to 4 mm. Which direction would this action potential be moving? b. Find and plot I;(x). At its peak, which is the direction of the current? c. Find and plot Ie(x). At its peak, which is the direction of the current? d. Find and plot Im(r). Interpret the sign of the peaks in relation to the direction of AP movement.