How would the velocity of action potential propagation chang

How would the velocity of action potential propagation change if you quadrupled the membrane permeability? For full credit you must have a quantitative answer?

Solution

The velocity of propagation of action potential is a function of to properties of the membrane, the membrane resistance(R_m) and membrane capacitance(Cm). The membrane resistance is the inverse of membrane permeability; higher the permeability, lower will be the resistance and vice versa. this means that if the permeability of the axon increases four times the resistance of membrane will decrease by 4, and so will be the propagation velocity. the velocity of propagation will be high if the resistance will high which means that the membrane permeability is decreased. so for the propagation of the action potential in the axon, there should be a decrease in membrane potential.