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

I'm only going to complete Part B. The other two are a bit easier and I believe you can do it! :D
Neighborhood A
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Year 1: 30 increased by 20% = 6 more homes.
Year 2: 36 increased by 20% = 7.2 more homes ... 7 more homes. You cannot round in these types of problems.
Year 3: 43 increased by 20% = 8.6 ... 8 more homes.
Year 4: 51 increased by 20% = 10.2 ... 10 more homes.
Year 5: 61 increased by 20% = 12.2 ... 12 more homes.
At the end of 5 years Neighborhood A will have 73 homes in total.

Neighborhood B
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Year 1: 45 +3 = 48
Year 2: 48 +3 = 51
Year 3: 51 +3 = 54
Year 4: 54 +3 = 57
Year 5: 57 +3= 60 homes
After 5 years Neighborhood B will have 60 homes.
Hope this helped! I will do Part A or Part C later if I have time and you still need assistance.