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dsp73
3 years ago
15

(05.03 HC) There are 30 homes in Neighborhood A. Each year, the number of homes increases by 20%. Just down the road, Neighborho

od 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.
Mathematics
1 answer:
borishaifa [10]3 years ago
7 0

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

For neighbourhood B: f(x) =  45 + 3x

B.

After five years;

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

Neighbourhood A  = \mathbf{30 \times  (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 \times  (1.2)^x= 45 + 3x}

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

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

x = 3.3

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

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