OpenStudy (anonymous):

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.

2 years ago
OpenStudy (anonymous):

@Kainui @mathway

2 years ago
OpenStudy (danjs):

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

2 years ago
OpenStudy (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^

2 years ago
OpenStudy (danjs):

ok...

2 years ago
OpenStudy (danjs):

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

2 years ago
OpenStudy (danjs):

30(1.2)^x = 40 + 3x

2 years ago
OpenStudy (anonymous):

I know but I dont know what number to start at

2 years ago
OpenStudy (danjs):

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

2 years ago
OpenStudy (danjs):

So recalculate part B for that one

2 years ago
OpenStudy (anonymous):

you sure? Okay so final houses=60

2 years ago
OpenStudy (danjs):

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

2 years ago
OpenStudy (anonymous):

its right; 45

2 years ago
OpenStudy (anonymous):

2 years ago
OpenStudy (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

2 years ago
OpenStudy (anonymous):

30(1.2)^5 does not equal 60

2 years ago
OpenStudy (anonymous):

@david422

2 years ago
OpenStudy (anonymous):

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

2 years ago
OpenStudy (anonymous):

y=30(1.2)^x

2 years ago
OpenStudy (anonymous):

The equation from part one

2 years ago
OpenStudy (anonymous):

@DanJS

2 years ago
OpenStudy (anonymous):

idk i just went off what your initial question was

2 years ago
OpenStudy (anonymous):

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

2 years ago
OpenStudy (anonymous):

@DanJS

2 years ago
OpenStudy (anonymous):

@ali2x2

2 years ago
OpenStudy (anonymous):

@Kainui

2 years ago
OpenStudy (anonymous):

@Afrodiddle @zepdrix

2 years ago
OpenStudy (danjs):

sorry back, here is the graph

2 years ago
OpenStudy (danjs):

the intersection is the point you need

2 years ago
OpenStudy (anonymous):

okay so when x=3.32, the two points intersect

2 years ago
OpenStudy (anonymous):

3.321 i meant

2 years ago
OpenStudy (danjs):

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

2 years ago
OpenStudy (anonymous):

okay, thanks!

2 years ago
OpenStudy (danjs):

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

2 years ago
OpenStudy (danjs):

welcome

2 years ago