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.

Part B: How many homes does Neighborhood A have after 5 years? How many does Neighborhood B have after the same number of years?

Part C: After approximately how many years is the number of homes in Neighborhood A and Neighborhood B the same? Justify your answer mathematically.

Question

Mathematics

Clark

4 April, 20:53

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.

Part B: How many homes does Neighborhood A have after 5 years? How many does Neighborhood B have after the same number of years?

Part C: After approximately how many years is the number of homes in Neighborhood A and Neighborhood B the same? Justify your answer mathematically.

+3

Answers (2)

Know the Answer?

Daniela Hines · Answer 1

A.

this is assuming it grows by 20% of the houses it has at that time (compound interest)

A (x) = 30 (1.2) ˣ⁻¹ or A (x) = 25 (1.2) ˣ

B (x) = 3 (x-1) + 45 or B (x) = 3x+42

B.

A (5) = 62.28 or about 62 homes

B (5) = 60

C.

this is tricky so I think it should have been only 20% of 30

start over

A.

20% of 30=6

A (x) = 6 (x-1) + 30 or A (x) = 6x+24

B (x) = 3 (x-1) + 45 or B (x) = 3x+42

B.

A (5) = 54 homes

B (5) = 60

C.

6x+24=3x+42

minus 3x

3x+24=42

minus 24 both sides

3x=18

divide by 3

x=6

after 6 years

both will have 63 homes

Demarion Mendoza · Answer 2

Part A

y=number of years (in both equations)

F (a) = 30 (1+r/n) ^y

r=.2 (20%)

n=1

F (b) = 45 + (3y)

Part B

A=74.6496 (personally I'd round to 74 because we are talking about an item that's not complete/useable yet, vs just a number if rounding is even required)

B=60

Part C

y=3.32 or approx 3 and 1/3 years

solve both and each neighborhood has about 55 houses

54.95 for a

54.96 for b