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

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.

anonymous · Answer

I think I have the answer to most of it if someone could review what i have

anonymous · Answer

Sure, I'll go over it.

anonymous · Answer

ok thank you

anonymous · Answer

part A i have f(x)= 30* 0.2x 
                     f(x)=45+3x

anonymous · Answer

which is nieghborhood A is gaining 6 houses which is 36 and nieghbor is gaining 3 house which is 48

anonymous · Answer

How did you get that first one? Because I'd go with a variation on compound growth. Or is the 0.2x to the power if x not multiplied by? So it's by 1.2, not 0.2.
Second one is great.

anonymous · Answer

ok that is maybe where i am confused

anonymous · Answer

how are you getting 1.2 are you adding 100% +20% =120% =1.2

anonymous · Answer

It's the right process, you just got the formula slightly wrong. It's
N$$N = N _{0} \times (\frac{ y }{ 1.00 })^{z}$$

anonymous · Answer

Yeah, that.

anonymous · Answer

So $$N _{0}$$ is the starting number, y is the percentage, and z is the number of years (or months, or whatever). I was wrong, it's 1 + y, not y divided by 1.

anonymous · Answer

So $$N = N _{0} \times ( 1 + y )^{z}$$

anonymous · Answer

How are you doing with part C ?

anonymous · Answer

It's just Lowest Common Factor.

anonymous · Answer

i get the concept but what is the No stand for part c im a little confused now

anonymous · Answer

No Stand? I don't see that.
All you have to do is find the lowest common factor and then justify it.

anonymous · Answer

can you explain hwo you got the N in the formula

anonymous · Answer

*how

anonymous · Answer

N? So the first N is the answer. You can write it the other way round if you want. The second N, with the subscript (the little O), is just the amount of stuff (money, or value, or in this case houses) you started with.

anonymous · Answer

oh ok so I can write it f(x)=30*(1+y)^2   or is this wrong too

anonymous · Answer

someone please help im confused now