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

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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

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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
part B put n=5 in the above formulas compound formula above give total no. of homes for Neighborhood A second formula correction \[a _{n}=a+nd\] \[a _{5}=45+3*5=?\]
Part C \[30\left( 1.2 \right)^n=45+3n\] find n

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Can anyone please give me the answer?
To all three parts?
I've been stuck on the same question for like ever and I just want to get it over with!
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.
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

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