Cory has 15 die-cast cars in his collection. Each year his collection increases by 20%. Roger has 40 cars in his collection. Each year he collects 1 additional car.

Part A: Write functions to represent Cory and Roger's collections throughout the years.

Part B: How many cars does Cory have after 6 years? How many does Roger have after the same number of years?

Part C: After approximately how many years is the number of cars that Cory and Roger have the same? Justify your answer mathematically.