Final answer:
The membrane potential of a cell will become more positive if the external concentration of potassium ions increases, since this reduces the concentration gradient and the driving force for K+ to leave the cell.
Step-by-step explanation:
If the extracellular K+ concentration increases dramatically, the membrane potential of the cell will become more positive. Normally, potassium ions (K+) are maintained at high concentrations within the cell, and the cell membrane is more permeable to K+ than to sodium ions (Na+), which are more plentiful outside the cell. When K+ ions diffuse out of the cell, they take positive charges with them, making the inside of the cell negatively charged relative to the outside. This creates the resting membrane potential. However, if the extracellular concentration of K+ increases, the concentration gradient for K+ across the membrane becomes shallower, reducing the driving force for K+ to leave the cell. Consequently, less positive charge leaves the cell, and the membrane potential becomes less negative or more positive. This effect on the membrane potential is due to the dependence of the resting potential on the K+ concentration gradient, as defined by the Nernst equation.