Moore's law: relationship between transistor count on an integrated circuit and minimum feature size
As a simple approximation, transistor count is determined by the number of transistors per unit area so it is inversely proportional to the area required for a single transistor. The area required is proportional to the square of the linear dimension. The feature size is a linear dimension, to the increase in transistors per unit area is proportional to the square of the feature size. Decrease the feature size to 70% of its original value and you double the number of transistors per unit area.