Answer:
Step-by-step explanation:
From the information given:
Neighbourhood A = 30 homes and the number increases by 20% each year
Neighbourhood B = 45 homes, and each year 3 new homes are built.
A.
The function representing the numbers of homes in Neighbourhood A and B are as follows:
For neighbourhood A: f(x) = 
For neighbourhood B: f(x) = 45 + 3x
B.
After five years;
Neighbourhood A has = 
Neighbourhood A = 
Neighbourhood A = 74.65 homes
Neighbourhood B: = 45 + 3(5)
Neighbourhood B: = 45 + 15
Neighbourhood B: = 60 homes
C.
To determine how many years the number of homes are the same for neighbourhood A and B, we need to equate both together.
i.e.



x = 3.3
Thus, after 3.3 years, the number of homes will be the same.