## anonymous one year ago 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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1. anonymous

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

2. anonymous

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

3. anonymous

Part C $30\left( 1.2 \right)^n=45+3n$ find n

4. anonymous

5. anonymous

To all three parts?

6. anonymous

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

7. anonymous

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.

8. anonymous

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