Final answer:
The statement is true; during the decay stage of a tornado, it often becomes elongated and narrow, resembling a rope, indicating the tornado is weakening.
Step-by-step explanation:
The statement that during the decay stage of a long-lived tornado, the tornado vortex takes on the shape of a rope is true. As tornadoes progress through their lifecycle, they often start with a wider funnel that is in contact with the ground. Over time, as they start to dissipate, they can stretch into a thinner, rope-like shape, signaling the tornado is weakening.
This rope stage can sometimes be one of the most dramatic parts of a tornado's life cycle visually and is a common characteristic of the tornado dissipation process.