Question

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.

Answer 1

@Kainui @mathway

Answer 2

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

Answer 3

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^

Answer 4

ok...

Answer 5

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

Answer 6

30(1.2)^x = 40 + 3x

Answer 7

I know but I dont know what number to start at

Answer 8

Oh, you have 40 for neighborhood B, it is 45

30(1.2)^x = 45 + 3x

Answer 9

So recalculate part B for that one

Answer 10

you sure? Okay so final houses=60

Answer 11

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

Answer 12

its right; 45

Answer 13

/?What number should I START with

Answer 14

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

Answer 15

30(1.2)^5 does not equal 60

Answer 16

@david422

Answer 17

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

Answer 18

y=30(1.2)^x

Answer 19

The equation from part one

Answer 20

@DanJS

Answer 21

idk i just went off what your initial question was

Answer 22

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

Answer 23

@DanJS

Answer 24

@ali2x2

Answer 25

@Kainui

Answer 26

@Afrodiddle @zepdrix

Answer 27

sorry back, here is the graph

Answer 28

the intersection is the point you need

Answer 29

okay so when x=3.32, the two points intersect

Answer 30

3.321 i meant

Answer 31

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

Answer 32

okay, thanks!

Answer 33

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

Answer 34

welcome