Question

Please Help?!

Answer 1

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 mathematically. (4 points)

Answer 2

Well let's see I think we could represent this is a linear function

we know we start out with 30 homes and each year it increases by 0.20. OR 20%

I thought we could represent this by saying the following.

\[30+30(*0.2)h = y_{number~of~homes)}\]

\[45+3h = y_{neighborhood~B}\]

not to sure about the first formula

@SolomonZelman help?

Answer 3

I'm wondering how you would be able to represent the growth by 20% each year because I guess you would have to account for the increase in number of homes.

Answer 4

I don't see a need in using h, a more precise variable would be t (or x), but that doesn't matter, and the formula is not exactly correct.

Answer 5

That 1st formula is an exponential actually.

Answer 6

If x increases by 20 percent every year, that means that you are taking 120% of x every year (right?). So in fact, every year you would be multiplying x times 1.20.

Answer 7

so that would be a linear function like y = m(x)+b? right

Answer 8

wouldnt**

Answer 9

yes, it is not a linear. It is an exponential.

Answer 10

\[y = 30x^{1.20}\]?

Answer 11

You have 30 houses initially.
Every year the number of houses increases by 20% (and that is that every year you have 120% of the houses, in comparison to the previous year). So, to get this growth in houses, the more precise equation would be,
\(\color{#000000}{ \displaystyle y=30(1.20)^{h+1} }\)

Answer 12

you are multiplying times 1.20 , h number of times (or h number of years, in this case). Since you take 120% every year.

Answer 13

This is not a power function.

Answer 14

And the formula for neighborhood B that you wrote is correct.

Answer 15

sorry why is it h+1 and not just h

Answer 16

Your initial value is 30, right?

Answer 17

yep

Answer 18

Oh, that is incorrect. I made a mistake, thanks for noticing

Answer 19

\(\color{#000000}{ \displaystyle y=30(1.20)^{h} }\)

Answer 20

I overthought here. Hehe

Answer 21

*points water gun to head* I'm completely confused, lol.

Answer 22

Let's attempt to settle this.

Answer 23

Ok, do you understand the formula for neig. B ?

Answer 24

I should have waited for her to respond lol before I asked

Answer 25

Noooo.

Answer 26

For neighborhood B you are given that you start from 45 houses, and every year the number of houses increases by 3.

Answer 27

For this reason greatlife44 wrote:
\(\color{#000000}{ \displaystyle y=45+3h }\)

Answer 28

making sense so far?

Answer 29

:)

Answer 30

okay, quick question. Is this for part one?

Answer 31

Yes, we are writing the functions that correspond to the scenarios given in part 1.

Answer 32

Oh okay okay

Answer 33

So, you get the formula for neigb. B?

Answer 34

nOt quite...

Answer 35

Ok, when I say that the number of houses starts from 45,
then I know that y=45.

however, each year the number of houses grows by 3.
So, after 1 year you add 1•3 number of houses,
after 2 years you add 2•3 number of houses,
after 7 year you add 7•3 number of houses,

and this way, after any "h" number of years, you add h•3 number of houses. So, to model the number of houses (y), after years (h), you will need to include the initial number of houses before any years had gone by, and the number of houses that the neigb. gains per year. This way you get:
`  y=45+3h  `

Answer 36

AHHHHH I get it now lol