I WILL FAN AND MEDAL!!!!!!!!!!!!!!!!
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 C: After approximately how many years is the number of cars that Cory and Roger have the same? Justify your answer mathematically. (4 points)

Question

I WILL FAN AND MEDAL!!!!!!!!!!!!!!!!
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 C: After approximately how many years is the number of cars that Cory and Roger have the same? Justify your answer mathematically. (4 points)

undeadknight26 · Answer

Well 20% of 15 is what.

sshayer · Answer

let x be the number of years
then
$$15(1+\frac{ 20 }{ 100 })^x=40 +1x$$
$$\left( \frac{ 6 }{ 5 } \right)^x=\frac{ 40 }{ 15 }+\frac{ x }{ 15 }$$
find x

sshayer · Answer

by hit and trial method after 6 years number of cars is almost the same.