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.