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

Neighborhood A: 30 homes and increases by 20% per year
Neighborhood B: 45 homes and increases by 3 per year.

N.A = 30 (1.20)^t
N.B = 45 + 3(t)

t = 5

N.A = 30(1.20)^5 = 30(2.48832) = 74.65 or 75
N.B = 45 + 3(5) = 45 + 15 = 60