MEDAL/FAN
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 C: After approximately how many years is the number of homes in Neighborhood A and Neighborhood B the same? Justify your answer mathematically.

- anonymous

- jamiebookeater

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- DanJS

Was part A and B to come up with the equations to model both those situations?

- anonymous

Part A:Neighborhood A:y=30(1.2)^x
Neighborhood B: y=40+3x
Part B: I just substitute x for 5.
Neighborhood A's work:
y=30(1.2)^5
y=30*2.48832
y=74.6494, or around 75 houses.
Neighborhood B's work:
y=40+3*5
y=40+15
y=55, so 55 houses
@DanJS my answers^

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## More answers

- DanJS

ok...

- DanJS

Part C wants you to figure the years X, when both are equal # houses

- DanJS

30(1.2)^x = 40 + 3x

- anonymous

I know but I dont know what number to start at

- DanJS

Oh, you have 40 for neighborhood B, it is 45
30(1.2)^x = 45 + 3x

- DanJS

So recalculate part B for that one

- anonymous

you sure? Okay so final houses=60

- DanJS

"Neighborhood B has 45 homes. Each year, 3 new homes are built ", less the prob is typed wrong

- anonymous

its right; 45

- anonymous

/?What number should I START with

- anonymous

20% of 30 is 6 so you could just use process of elimination.
3*5=15 15+45=60
5*6=30 30+30=60
so after 5 years they will be the same

- anonymous

30(1.2)^5 does not equal 60

- anonymous

- anonymous

where did you get 30(1.2)^5??

- anonymous

y=30(1.2)^x

- anonymous

The equation from part one

- anonymous

- anonymous

idk i just went off what your initial question was

- anonymous

well the equations are:
Neighborhood A:y=30(1.2)^x
Neighborhood B: y=45+3x

- anonymous

- anonymous

- anonymous

- anonymous

- DanJS

sorry back, here is the graph

##### 1 Attachment

- DanJS

the intersection is the point you need

- anonymous

okay so when x=3.32, the two points intersect

- anonymous

3.321 i meant

- DanJS

yes, when 3.32 years have passed , both have same number of houses at near 55

- anonymous

okay, thanks!

- DanJS

i just asked a question about that form of equation...

- DanJS

welcome

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