Final answer:
The protein that stretches the ER membrane as a cell grows is kinesin, which is a motor protein that transports cellular cargo along microtubules.
Step-by-step explanation:
As a cell grows, the microtubule-associated protein that pulls the ER membrane outward, stretching it like a net, is kinesin. Kinesin is a motor protein that uses the energy provided by ATP hydrolysis to move along microtubule tracks within the cell. It is involved in the transport of various cellular cargoes, including organelles such as the endoplasmic reticulum.