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.

Answer 1

Part A) n.a = 30(1.20)^t

N.B = 45 + 3(t)

Part B) N.A = 30(1.20)^5 30(2.48832) = 75

n.b = 45+3(5)=60

Part C) 30(1.2)^x= 45+3x

x = 3.32079
in the third year the number of houses are the same