Active transport of K+ allows the cell to survive by increasing the concentration of solutes and avoiding dehydration.
Explanation:
A hypertonic solution is a solution which has a higher concentration of solutes than the inside of the cell. This solution also has lower concentration of solvent (water)
When a cell is exposed to this type of solution, water leaves the cell by osmosis, since water will always go from low concentration of solute to high concentration of solutes. In other words, from high concentration of water to low concentration of water. If the difference in concentration (gradient) is very high, the cell can dehydrate and die.
By using ATP (energy) to take ions in, E. coli is able to increase the concentration of solutes inside the cell and thus, reduce the gradient. When the concentration inside the cell equals that of the solution, water stops flowing out of the cell, dehydration is prevented and the cell can survive.