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.
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.
I just need part c!

Answer 1

let's name "x" the number of years.

we know that
`15 +15*1.20^(x) =40+x`

let's try after 5 years: Roger would have 45 cars and Cory 52 ( i just guessed 5, and then I calculated 15 +15*1.20^{5} ): so, no, it has to be less than 5.

let's try 4:

Roger will have 44, and cory 15+31=45, so that's quite good asnwer!

Let's try with 3:

Roger will have 43, and Cory 15+ 25=40,

so 4 years are better: after approximately 4 years.

(perhaps a better strategy would be to just calculate after each year starting at 1 and going up...)