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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.

Verified Answer :

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Part A:
For Roger: \(y=x+40\)
For Cory: \(y=15 (1.2)^{x}\)
where y is the total  number of cars each boy collects over the year, x as the number of years passed.

Part B:
For Roger: 46
For Cory: 44.79~ 45 cars

Part C:
Here, we are trying to find the number of years (x) where Cory and Roger have the same number of cars.
By equating Roger and Cory's functions, we can solve for x
\(x+40=15 (1.2)^{x}\).
Since we cannot solve the value of x directly, we use trial and error to estimate the year.
When x=1
\(41 eq 18 \\\)
When x=2
\(42 eq 21.6\)
When x=3
\(43 eq 25.92\)
When x=4
\(44 eq 31.10\)
When x=5
45=/=37.3
When x=6
46=/=44.8
When x=7
47=/=53.7

The years that pass by before  Cory and Roger have nearly the same number of cars is 6.

Answer:

Step-by-step explanation:

Part A:

For Roger:

For Cory:

where y is the total number of cars each boy collects over the year, x as the number of years passed.

Part B:

For Roger: 46

For Cory: 44.79~ 45 cars

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