42.0k views
4 votes
(05.03 HC) 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.

User Gradient
by
6.3k points

1 Answer

4 votes

Answer:

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) =
\mathbf{30 * (1.2)^x}

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

B.

After five years;

Neighbourhood A has =
\mathbf{30 * (1.2)^x}

Neighbourhood A =
\mathbf{30 * (1.2)^5}

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.


\mathbf{30 * (1.2)^x= 45 + 3x}


\mathbf{ (1.2)^x= (45 + 3x)/(30)}


\mathbf{ (0.4)^x= (15 + x)/(10)}

x = 3.3

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

User Nakima
by
6.9k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.