Question

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 1

help please? i have the equation just need help solving

Answer 2

@phi

Answer 3

@mathstudent55

Answer 4

@dan815

Answer 5

@xapproachesinfinity

Answer 6

it sounds like a geometric series.

Answer 7

i think its
an=a1r^(n-1)

Answer 8

you need numbers for a1, and r
any ideas?

Answer 9

a17=4r^(18-1) ?

Answer 10

ok what is r ?

Answer 11

hint 1.13 times as many villagers.

Answer 12

a1=1.13

Answer 13

1.13*4?

Answer 14

let number of towns be tlet number of villagers be v

Each town he has allows him to create 1.13 times as many villagers,implies
t=1.13v

then since he starts with 4 villagers we have
17=1.13(v+4)⟹v=171.13−4

in general
t=1.13(v+4)⟹v=t1.13−4

Answer 15

use the equation t=1.13(v+4), plug in for t and solve for v

Answer 16

@topstryker

Answer 17

did this help

Answer 18

its hard for me to follow... can we try and fill in the geometric series formula?...

Answer 19

Well the way I see it is he started with 4 villager so I would see the equation to be

1.13x times 17+4 would equal the amount of villagers he could have which would be 23.21 as for the equation it would be 1.13x times 17 plus four equals the number of villagers total

Answer 20

@lupita1995

Answer 21

yes

Answer 22

would that answer the question you think?
@lupita1995

Answer 23

i think so

Answer 24

*** 1.13*4***
that gives you the answer after one "step"
Each town he has allows him to create 1.13 times as many villagers

so he starts with 1 town with 4 people
his next town has 1.13 * (1.13*4) = 1.13^2 * 4 or 4*1.13^2
for the next town we multiply by 1.13 to get the number of people in this town
(not sure how we fractions of a person... which makes this a very goofy question)

but ignoring how goofy it is, we get
an= 4 * 1.13^(n-1)

when n = 1 (the first town) we get 4* 1.13^(1-1)
1.13^0 is 1 (anything to the 0 power is 1), and we get 4 people.

Answer 25

1.13(17+4) does that answer the question? =23.21? @phi

Answer 26

no. read my post carefully

Answer 27

where does the 17 towns come into?

Answer 28

the geometric series is defined for any n (n is the number of towns)

\[ a_n = 4 \cdot 1.13^{n-1} \]

Answer 29

and n=17? @phi

Answer 30

@jdoe0001

Answer 31

@SolomonZelman

Answer 32

** and n=17 ***
yes, if you want to find the number of people he can create with 17 towns, use n=17 in the formula posted above.