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.

Part A:
For Roger: 
For Cory: 
where y is the total  number of cars each boy collects over the year, x as the number of years passed.

Part B:
For Roger: 46
For Cory: 44.79~ 45 cars

Part C:
Here, we are trying to find the number of years (x) where Cory and Roger have the same number of cars.
By equating Roger and Cory's functions, we can solve for x
.
Since we cannot solve the value of x directly, we use trial and error to estimate the year.
When x=1

When x=2

When x=3

When x=4

When x=5
45=/=37.3
When x=6
46=/=44.8
When x=7
47=/=53.7

The years that pass by before  Cory and Roger have nearly the same number of cars is 6.

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