Final answer:
An increased extracellular K+ concentration would lead to a slower falling phase of the action potential, as K+ would leave the neuron more slowly due to a reduced concentration gradient. This manipulation would not directly affect the rising phase, which is driven by Na+ inflow.
Step-by-step explanation:
When considering how the action potential of a squid giant axon might change in an extracellular solution with a 10% higher concentration of K+ ions, we need to look at the effect of this concentration change on the diffusion of K+ ions during the repolarization phase of the action potential. In a normal setting, the concentration gradient for K+ across the membrane is the driving force for its efflux, leading to the repolarization of the neuron after the peak of the action potential.
If the external concentration of K+ is increased, the concentration gradient of K+ across the membrane is reduced, which would decrease the driving force for K+ to exit the neuron. Consequently, the -falling phase of the action potential would be slower because K+ would exit the neuron at a reduced rate, delaying the repolarization process (so Option 4 is correct). However, this change in K+ concentration would not directly affect the rising phase of the action potential, which is primarily driven by Na+ inflow. Therefore, there would be no expected acceleration in the rising phase (so Options 1 and 2 are incorrect). As the falling phase is slower, the return to resting membrane potential would also be delayed, making it less likely that hyperpolarization would be any faster. Therefore, Option 3 is incorrect as well.