Final answer:
The example of molecular movement across a membrane through active transport is proton pumps moving hydrogen ions out of the cell against a concentration gradient, which requires energy usually from ATP.
Step-by-step explanation:
An example of molecular movement across a membrane through active transport is when proton pumps move hydrogen ions out of the cell against a concentration gradient. Unlike passive transport, which allows molecules to move down the concentration gradient without the use of energy, active transport requires energy, commonly in the form of adenosine triphosphate (ATP). Proton pumps, such as those found in cellular membranes, work by using ATP to transport protons (hydrogen ions) across the membrane, creating a concentration gradient.
Channel proteins binding with extracellular solutes and releasing them inside the cell describe facilitated diffusion, hydrocarbons entering the cell by dissolving in the lipid bilayer of the membrane relate to passive diffusion, and vesicles carrying waste products fusing with the membrane during endocytosis is a form of vesicular transport, specifically exocytosis if it involves waste removal.