Math check!

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.

Question

Math check! 

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.

anonymous · Answer

Part A: Write functions to represent Cory and Roger's collections throughout the years.

Answer: Cory: y = 15(1.2)^ x
                Roger y = x + 40

anonymous · Answer

looks good to me

anonymous · Answer

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

anonymous · Answer

Rodger will have 46 cars while Cory will have 55

anonymous · Answer

the 46 is certainly right 
need a calculator for the other one

anonymous · Answer

that is not what i get 
be careful how you enter it

anonymous · Answer

what did you get?

anonymous · Answer

Wait... would it be 52?

anonymous · Answer

this is what i got http://www.wolframalpha.com/input/?i=15%281.2%29^6

anonymous · Answer

okay so it would have been 44

anonymous · Answer

depends on how you round, but  i guess so if you round down

anonymous · Answer

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

anonymous · Answer

cory:
y = 15 * 1.2^x 

roger:
y = 40 + x 

the functions intersect when x = 6.16599

anonymous · Answer

this requires a calculator, but when you approximate i guess they may want you to round

anonymous · Answer

i get the same thing you do

anonymous · Answer

yeah, Ive been having a hard time with this part

anonymous · Answer

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

anonymous · Answer

that is the same as what you just did

anonymous · Answer

approximately 6 i would say

anonymous · Answer

After 6 years Rodger will have 40 cars while cory will have 44?

anonymous · Answer

46

anonymous · Answer

after 6 years roger will have 46 right?

anonymous · Answer

yeah, i have to find when they would have the same amount of cars

anonymous · Answer

it will not be a whole number of years 
at 6 roger has 46 and cory has 44.8 or so
but after 7 years roger will have 47 and cory will have $15(1.2)^7=53.74$ cars so year 6 is the closest

anonymous · Answer

Okay, thank you! I've been stuck on this all day.