Final answer:
Using the sodium-potassium pump's ratio of three Na+ out for every two K+ in, we can calculate the ion concentration changes after 10, 30, and 40 cycles. After 10 cycles: 70 Na+ and 45 K+; after 30 cycles: 10 Na+ and 85 K+; after 40 cycles, the calculation shows a negative number of Na+ ions, which is not possible, indicating a limit to the pump's function without additional Na+ supply.
Step-by-step explanation:
The question pertains to biology, specifically the function of the sodium-potassium pump in animal cells. To determine the number of Na+ and K+ ions inside the cell after a given number of pump cycles, we can apply the ratio of ions moved by the pump: three Na+ ions out for every two K+ ions in. This is pivotal for maintaining the electrochemical gradient across the cell membrane.
Initially, there are 100 Na+ ions and 25 K+ ions inside the cell. After one cycle, the cell will lose 3 Na+ ions and gain 2 K+ ions. Thus, the changes can be represented as:
- Na+ ions change per cycle: -3
- K+ ions change per cycle: +2
Let's calculate the changes after 10, 30, and 40 cycles:
- After 10 cycles: (100 - 3(10)) Na+ ions = 70 Na+ ions, (25 + 2(10)) K+ ions = 45 K+ ions
- After 30 cycles: (100 - 3(30)) Na+ ions = 10 Na+ ions, (25 + 2(30)) K+ ions = 85 K+ ions
- After 40 cycles: (100 - 3(40)) Na+ ions = -20 Na+ ions which is not possible, hence it indicates that the pump cannot function that many times without additional Na+ ions being available inside the cell, (25 + 2(40)) K+ ions = 105 K+ ions
It is important to note that the sodium-potassium pump requires ATP to function, and it is essential for nerve cells as it maintains an electrical gradient.