Question

Andrea is designing the seating arrangement for a concert in her local park. To give everyone a good view, each row must have 4 more seats than the row before it, and the 1st row can only have 10 seats. Help Andrea plan the rest of the seating by solving for how many seats are in row 20. Then explain to Andrea how to create an equation to predict the number of seats in any row. Show your work, and use complete sentences.

Answer 1

@ganeshie8

Answer 2

so we have 10 seats in the first row

Answer 3

yes

Answer 4

And `each row must have 4 more seats than the row before it`

Answer 5

can you guess how many seats the `second` row will have ?

Answer 6

14

Answer 7

so wouldn't you use a sequence formula

Answer 8

Yes.

10, 14, 18, ...

See the pattern ?

Answer 9

yes

Answer 10

What kind of sequence is that ?

Answer 11

arithmetic?

Answer 12

Yep, find out the `first term` and `common difference`

Answer 13

10 and 4

Answer 14

\(a_1 = 10\)
\(d = 4\)

https://www.chilimath.com/algebra/intermediate/arith/images2/labelled-parts-of-arithmetic-sequence-formula.png

Answer 15

a20=10+(20-1)4

Answer 16

Looks good

Answer 17

so 86

Answer 18

Perfect!

Answer 19

James has decided to start saving for a cruise over the summer. His money is currently in the local bank, modeled by the function s(x) = 102. He is able to do work around the neighborhood to earn extra money and that function would be a(x) = 8(x + 2), where x is measured in hours. Explain to James how he can create a function that combines the two, and describe any simplification that can be done.

Answer 20

thats the next one sorry it took so long to reply

Answer 21

@ganeshie8

Answer 22

Hey still here ?

Answer 23

yes

Answer 24

What's his current money in the local bank ?

Answer 25

102

Answer 26

Yes, that is his savings so far.

Answer 27

And if he works for `x` hours, he gets `8(x+2)`

Answer 28

yes

Answer 29

yes

Answer 30

So how much total money will he be having ?

Answer 31

8(x+2)+102

Answer 32

Looks good. Simplify

Answer 33

8x+118

Answer 34

Yep!

Answer 35

didn't think it was that easy lol word problems confuse me a lot

Answer 36

Chase has been playing a game where he can create towns and help his empire expand. Each town he has allows him to create 1.13 times as many villagers. The game gave Chase 4 villagers to start with. Help Chase expand his empire by solving for how many villagers he can create with 17 towns. Then explain to Chase how to create an equation to predict the number of villagers for any number of towns. Show your work and use complete sentences.

Answer 37

They confuse everyone haha. We just need to spend more time reading the problem multiple times till something makes sense ..

Answer 38

so he starts with 4

Answer 39

Could you post that in a new thread ?

Answer 40

yes

Answer 41

Okay wait, lets finish this here

Answer 42

is it a geometric sequence?

Answer 43

cause it increases 1.13 times per village

Answer 44

and the nth term would be 17?

Answer 45

would you use the same formula as the first or no cause its geometric?.

Answer 46

This problem is a bit confusing. If it helps, think of human population as virus - they keep multiplying.

Answer 47

first term = 4

Answer 48

common ratio seems to be 1.13

Answer 49

looks you have to find the 17th term

Answer 50

remember the geometric sequence formula ?

Answer 51

http://study.com/cimages/multimages/16/geometric-sequence-general-rule.jpg

Answer 52

a17=4(1.13^16)

Answer 53

28.26?

Answer 54

looks good to me

Answer 55

Tommy has $350 of his graduation gift money saved at home, and the amount is modeled by the function h(x) = 350. He reads about a bank that has savings accounts that accrue interest according to the function s(x) = (1.04)x − 1. After combining the two functions, his new function is g(x) = 350(1.04)x − 1. Using complete sentences, explain what this new function means.

Answer 56

Please put that in a new question