Question

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. (4 points)
Part B: How many cars does Cory have after 6 years? How many does Roger have after the same number of years? (2 points)
Part C: After approximately how many years is the number of cars that Cory and Roger have the same? Justify your answer mathematically. (4 point

Answer 1

I already have Part A, but i don't know how to finish solving it.
Part A:
cory's: y=15(1.2)^x
roger: y=x+40

Answer 2

x represents the year, and y represents the number of cars in the collection.
For part B, plug in 6 for x in both functions and find y.

Answer 3

For part C:
Cory's collection starts smaller but grows faster, so it will eventually catch up to Roger's collection.
To find when it will catch up, do this.
Let x = 1, and solve both functions for y.
Then let x = 2, and solve both functions for y.
Keep doing this with x = 3, x = 4, etc., until eventually, Cory's collection will be larger.
The time in which Cory's collection catches up to Roger's collection is between the highest value of x that Cory's collection is still smaller and the lowest value of x in which Cory's collection is already larger.
If you want to know the exact value of x, then set the two functions equal to each other, and solve for x.