Question

HELP?!

Answer 1

How do you show growth?

Answer 2

For example, if the growth is a certain percentage each year, what equation shows growth?

Answer 3

Let's say the growth is 10%. Since 100% + 10% = 110% = 1.1, then each year, multiply the previous year's amount by 1.1
Year 0 a
Year 1 1.1a
Year 2 1.1(1.1a) = 1.1^2 * a
Year 3 1.1(1.1^2)a) = 1.1^3 * a
Year x 1.1^x * a

Answer 4

In your case, the growth is 20%, so we use 1.2

Neighborhood A
\(y = 30 \times 1.2^x\)

Answer 5

and I would just replace x with 5?

Answer 6

In Neighborhood B, you start with 45 and the growth is linear, so its:
Year 0 45 houses
Year 1 45 + 3 * 1
Year 2 45 + 3 * 2
Year 4 45 + 3 * 3
etc.
Year x 45 + 3 * x


\(y = 45 + 3x\)

Answer 7

Part A.

Neighborhood A. \(y = 30 \times 1.2^x\)

Neighborhood B. \(y = 45 + 3x\)

Answer 8

Part B.
Let x equal 5 in each of the two functions above to find the number of homes in the two neighborhoods after 5 years.

Answer 9

Part C.
Set the two functions equal and solve for x.

Answer 10

so y=30*1.2^5 and y=45+3(5) for B?

Answer 11

Yes, and evaluate each expression.

Answer 12

y=74.6496
y=60

Answer 13

Good.
75 & 60

Answer 14

Notice that Neighborhood A started with 30 homes and B with 45.
By year 5, Neighborhood A already has more homes than B.
This gives you a hint as to the solution of part C.

Answer 15

what would I set my function equal to?

Answer 16

would I make a function table and use the formula until I get the same number of houses?

Answer 17

For Part C?

Answer 18

yes

Answer 19

\(30 \times 1.2^x = 45 + 3x\)

Answer 20

ohhh ok... and so that's all I need for part c, is to solve that?

Answer 21

You can use a table.
The hint I mentioned above is that since by year 5, Neighborhood A already has more homes than Neighborhood B, that means the year they have the same number of homes is between years 0 and 5.

Answer 22

Yes, up need to solve the equation, but your idea of letting x = 1, 2, 3, 4, 5 is good.

Answer 23

Make a table and see when Neighborhood A overtakes B.

Answer 24

awee yes I get it now

Answer 25

Are you given choices?

Answer 26

no it's open response

Answer 27

I'm making a table rn

Answer 28

OK. Then do what you mentioned above. Make a table.

Answer 29

We already know this: