The organelle that would be present in large numbers in a cell that actively transports a lot of glucose across its membrane is the mitochondria.

Here's why:

* Active transport requires energy: Moving glucose against its concentration gradient (from an area of low concentration to high concentration) requires energy. This energy is supplied by ATP (adenosine triphosphate).

* Mitochondria are the powerhouses of the cell: Mitochondria are responsible for cellular respiration, the process that produces ATP.

* Higher energy demand: A cell actively transporting a lot of glucose needs a lot of energy to power the pumps that facilitate this transport. Therefore, it would have a higher demand for ATP, which means it needs more mitochondria.

Example: Cells lining the small intestine actively transport glucose from the lumen of the gut into the bloodstream. These cells have a high density of mitochondria to support this energy-intensive process.