There are 30 homes in neighborhood a. each year, the number of homes increases by 20%. just down the road, neighborhood b has 45 homes. each year, 3 new homes are built in neighborhood b.

part a: write functions to represent the number of homes in neighborhood a and neighborhood b throughout the years.
part b: how many homes does neighborhood a have after 5 years? how many does neighborhood b have after the same number of years?
part c: after approximately how many years is the number of homes in neighborhood a and neighborhood b the same? justify your answer mathematically.