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.

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.

sshayer · Answer

for Cory
cars after  x years$$=15\left( 1+\frac{ 20 }{ 100 } \right)^x=15(1.20)^x$$
for Rogers=40+1x=40+2x (after x years)
after 6 years for put x=6
C. $$15\left( 1.2 \right)^x=40+x$$
by hit and trial method x=6 nearly

need.answers · Answer

I don't understand the part you put that's dealing with Roger.

need.answers · Answer

Like 40+1x=40+2x?

sshayer · Answer

40+1=41
40+2=42
..................
40+6+46

sshayer · Answer

correction
40+6=46

sshayer · Answer

it is wrong typed ,it is 40+x not 40+2x

need.answers · Answer

So 40+2x is the function to represent Roger?

need.answers · Answer

40+x *

sshayer · Answer

no,it is 40+x

need.answers · Answer

Ah okay. So to continue this and solve the two function, I have to place 6 in x?