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.
Answers
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
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
Since we cannot solve the value of x directly, we use trial and error to estimate the year.
When x=1
When x=2
When x=3
When x=4
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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y = (x - 7)² - 9
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if it helps you any just translate 40% to .4 just do 40/100, there are two zeros in 100 so move the decimal of 40. over two places 40%=40/100=.4
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