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 points)

Answer 1

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 points)

15(.20)(4)+15=37

15X20%=3 additional cars each year.

3 cars per year times 4 years equals 12 additional cars in 4 years.

If he started with 15 cars and adds the 12 cars he collects in the next 4 years, he will have a total of 27 cars in 4 years. B) in 6 years Cory will have collected 6 additional cars for a total of 27 + 6 = 33 cars. 13 years = 54 cars.

C. If Roger has 40 cars now and collects 1 additional car each year then at the end of 13 years Roger will have 53 cars and Cory will have 54 cars.

Explanation:

Answer 2

15(.20)(4)+15=37

15X20%=3 additional cars each year.
3 cars per year times 4 years equals 12 additional cars in 4 years.
If he started with 15 cars and adds the 12 cars he collects in the next 4 years, he will have a total of 27 cars in 4 years. B) in 6 years Cory will have collected 6 additional cars for a total of 27 + 6 = 33 cars. 13 years = 54 cars.
C. If Roger has 40 cars now and collects 1 additional car each year then at the end of 13 years Roger will have 53 cars and Cory will have 54 cars.