Final answer:
The ignition of all exposed surfaces is the common element of flashover indicating the transition from the growth stage to fully developed stage; this involves the interconnected factors of temperature, fuel density, and time.
Step-by-step explanation:
The common element of flashover that represents the shift from the growth stage to the fully developed stage in fires is the ignition of all exposed surfaces. A flashover is a critical event in fire development marked by the near-simultaneous ignition of everything in the room. This phenomenon is heavily influenced by the three factors of temperature, density of the fuel, and time.
These three factors are interconnected; a deficiency in one can be offset by the others. An increased surface area of fuel could lead to a more rapid fire spread as demonstrated by the burning characteristics of smaller twigs compared to a large log, owing to the greater surface area provided by the twigs. When ignition occurs, the energy released by the fire becomes self-sustaining, leading to the rapid onset of a fully developed fire. This underscores the importance of controlling these variables to prevent such disasters.