Question

There are 30 homes in Neighborhood A. Each year, the number of homes increases by 20%. Just down the road, Neighborhood B has 45 homes. Each year, 3 new homes are built in Neighborhood B.

Part A: Write functions to represent the number of homes in Neighborhood A and Neighborhood B throughout the years. (4 points)
Part B: How many homes does Neighborhood A have after 5 years? How many does Neighborhood B have after the same number of years? (2 points)
Part C: After approximately how many years is the number of homes in Neighborhood A and Neighborhood B the same? Justify your answer mathematically. (4 points)

Answer 1

Part A

f(x)=30∗0.2xandf(x)=45+3x
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Part B

f(x)=30+0.2(5)f(x)=45+3(5)
Neighborhood A and neighborhood B both have 60 houses after 5 years

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Part C

1 year
A=36
B=48

2 years
A=42
B=51

3 years
A=48
B=54

4 years
A = 54
B = 57

5 years
A = 60
B= 60