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 mathema

Answer 1

A.\[no.~ of~ homes~after~n ~years=30(1+\frac{ 20 }{ 100 })^n\]
for B
\[a _{n}=a+\left( n-1 \right)d\]
where a=45,d=3,n= no. of years

Answer 2

part B
put n=5 in the above formulas
compound formula above give total no. of homes for Neighborhood A
second formula correction
\[a _{n}=a+nd\]
\[a _{5}=45+3*5=?\]

Answer 3

Part C

\[30\left( 1.2 \right)^n=45+3n\]
find n

Answer 4

Can anyone please give me the answer?

Answer 5

To all three parts?

Answer 6

I've been stuck on the same question for like ever and I just want to get it over with!

Answer 7

Part C
divide by 3
\[10(1.2)^n=15+n\]
for n=1
10*1.2=15+1
12=16
for n=2
10*1.44=15+2
14.4=17
for n=3
\[10\left( 1.2 \right)^3=15+3,17.28=18\]
for n=4
\[10\left( 1.2 \right)^4=15+4,20.73=19\]
so approximately after 3 years,no. of houses is same.

Answer 8

part B after 5 years
no. of houses in neighborhood A\[=30\left( 1.2 \right)^5=75.93=76 \approx.\]
no. of houses in neighborhood B=45+3*5=45+15=60