Answer:
Facilitated diffusion.
The cell with mutated membrane proteins can not transport calcium ions. Simple diffusion does not use membrane proteins to transport the substances.
Step-by-step explanation:
Simple diffusion differs from facilitated diffusion in not using any membrane protein to transport the substances. Both simple and facilitated diffusion move the substances down their concentration gradient in a passive process.
However, facilitated diffusion makes use of integral membrane proteins to allow the charged or polar molecules to cross the membrane. These integral membrane proteins serve as channel or carrier and allow the polar and charged substances to cross the non-polar core of the membrane.
Calcium ions are charged particles and can not cross the non-polar core of the membrane. The cells with mutated membrane-bound proteins are not able to transport these ions. This suggests that calcium ions were moved across the membrane by facilitated diffusion through the wild type membrane-bound protein.