Question

Please help quickly! and Correctly. :)

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)

(10 points)

Answer 1

We know that:

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.

Neighbourhood A and B are as follows:

For neighbourhood A: f(x) =

For neighbourhood B: f(x) = 45 + 3x

B.

Over 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.

So x= 3.3

so, hence after 3.3 years, the number of homes will be the same.

Explanation:

Hope this helped, good luck