John has two sisters and two brothers. three of the five children in the family have dark brown hair, one has red hair, and one has light brown hair. the variation in hair color is due to the input of multiple genes. what pattern of inheritance is exhibited here?

Polygenetic inheritance
This type of inheritance is controlled by a group of epi-static genes which regulate expression of one phenotypic trait, which is hair color in this case. Such genes are often large in quantity but small in effect. These genes could also be pleiotropic as well. Polygenes also exist in other organisms apart from humans. 

Rna polymeras should attache to the promoter.