Final answer:
The steepness of the concentration gradient affects the rate of transport by determining the speed of diffusion; a steeper gradient results in a faster rate, while a gradient close to equilibrium slows down the rate.
Step-by-step explanation:
The steepness of the concentration gradient significantly influences the rate of transport across a membrane. When there is a large difference in concentration between two areas (steep gradient), diffusion occurs more rapidly because many more molecules move from an area of higher concentration to one of lower concentration. Conversely, as the concentration gradient decreases and approaches equilibrium, the rate of diffusion correspondingly becomes slower since there is less of a driving force for the movement of molecules.
Furthermore, when carrier proteins are involved in facilitated transport, they can become saturated if all the bonding sites are occupied, and increasing the concentration gradient further at this point will not increase the rate of transport. Each molecule diffuses down its own concentration gradient independent of others, and this process can release free energy, depending on the relative concentrations of the solutes involved.