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

n=17

Answer 2

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 3

okay thank you so much

Answer 4

this is super helpful

Answer 5

welcome