Question

active transport is most useful when...
a cell needs to move materials against the concentration gradient.
a cell has too much water, but the concentration of water outside the cell is higher than inside the cell.
a cell needs potassium, but the concentration inside the cell is higher than outside the cell.
all of these.

Explanation:

Active transport is a process that requires energy (usually in the form of ATP) to move substances against their concentration gradient (from an area of lower concentration to an area of higher concentration).

• For the first option: Moving materials against the concentration gradient is the key function of active transport.
• For the second option: If a cell has too much water and water outside is higher (so water would tend to move in by osmosis, a passive process), but if the cell wants to expel water against the gradient (since water is moving in by passive means but cell needs to get rid of it when it has too much, which would be against the gradient), active transport could be involved (e.g., in some cells with water - expelling mechanisms).
• For the third option: If a cell needs potassium and the concentration inside is already higher (so to take in more potassium, it has to move it against the gradient), active transport is needed.

Since all the scenarios (moving against a gradient in each case) can be addressed by active transport.

Answer:

all of these.