Question

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)

Answer 1

Part A)

y = total houses, x = number of years

Neighborhood A y = 30*(1.20)^x

Neighborhood B : y = 45 +3x

Part B) neighborhood A has : 30 *1.2^5 = 74.65 = 75 houses

neighborhood B has: 45 +3(5) = 45 +15 = 60 houses

Part C)

30* 1.2^x = 45 +3x =

x = 3.3

check:

30 *1.2^3.3 = 54.75 = 55

45 + 3(3.3) = 45+9.9 = 54.9 =55

so 3.3 years round to 3 years

Explanation:

Answer 2

Part A)

y = total houses, x = number of years

Neighborhood A y = 30*(1.20)^x

Neighborhood B : y = 45 +3x

Part B) neighborhood A has : 30 *1.2^5 = 74.65 = 75 houses

neighborhood B has: 45 +3(5) = 45 +15 = 60 houses

Part C)

30* 1.2^x = 45 +3x =

x = 3.3

check:

30 *1.2^3.3 = 54.75 = 55

45 + 3(3.3) = 45+9.9 = 54.9 =55

so 3.3 years round to 3 years