True, but you forget that it's still negative and equilibrium potential is +50mv so there is still strong movement for Na+ into the cell. So, your argument doesn't hold. Well done guys.
I'm not at home right now, so I don't have access to a textbook, but I believe what eikenhein and I said is true. I realize that the membrane potential is still negative, but the thing is, the more depolarized you are from the normal membrane potential, the higher the probability is that the slow-acting inactivation gates on Na+ channels are closed. If these gates are closed, Na+ ions cannot move into the cell; it doesn't matter if the potential is closer to 0.
So, with slight depolarization, as eikenhein mentioned, it would be easier to fire an AP (because slight depolarization is not enough to cause closure of the Na+ inactivation gates). But once you get more depolarization, the inactivation gates on some Na+ channels are more likely to be closed; this makes it harder to fire action potentials (since Na+ ions cannot move inwards).
If you had specified in your original question that the increase in extracellular K+ was only slight, then I would agree with you that I'm wrong. Hope this clears up my thought process behind answering the question the way I did. Like I mentioned, I'm not home right now and don't have access to a textbook, but this was how I understood the process when I first learned it. If anything is wrong with my explanation, feel free to point it out.
😛
Edit: I'm back home and I looked into the Costanzo physiology textbook. Here's a description regarding a case study of hyperkalemia in the section discussing action potentials:
"When the blood [K+] is elevated, the concentration gradient across the cell membrane is less than normal; resting membrane potential will therefore be less negative (i.e., depolarized). It might be expected that this depolarization would make it easier to generate action potentials in the muscle because the resting membrane potential would be closer to threshold.
A more important effect of depolarization, however, is that it closes the inactivation gates on Na+ channels. When these inactivation gates are closed, no action potentials can be generated, even if the activation gates are open. Without action potentials in the muscle, there can be no contraction."
So yea, there cannot be a strong inward Na+ current if the gates are closed. Like eikenhein mentioned previously,
slight depolarization would make it easier to depolarize the cell further (because it wouldn't affect the Na+ channels adversely), but if the depolarization is beyond a slight depolarization (ie. a much higher extracellular K+), further depolarization will be
inhibited due to the closing of these inactivation gates; there cannot be an inward Na+ current if the gates are closed! You have to take into account the properties of the ion channels and not just the fact that the inside of the cell is still negative. Hope this helps.