Question

Brian has been playing a game where he can create towns and help his empire expand. Each town he has allows him to create 1.17 times as many villagers. The game gave Brian 8 villagers to start with. Help Brian expand his empire by solving for how many villagers he can create with 16 towns. Then explain to Brian 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

@phi

Answer 2

*** Each town he has allows him to create 1.17 times as many villagers.***

that sentence means if you have 1 town, then you can create 1.17 * x
(where x is the starting number of villagers)
if you have 2 towns , you can create 1.17*1.17*x
if you have 3 towns, then 1.17*1.17*1.17*x or \(1.17^3 \cdot 8\)

Answer 3

o ok

Answer 4

any idea what the equation is for 12 towns ?

Answer 5

1.17^12*8?

Answer 6

yes. to make it easier to understand, I think we should write it a
\[ 8 \cdot 1.17^{12} \]

(1.17^12*8 is correct, but we might read it wrong)
we need a calculator to find the answer.

Answer 7

52.6

Answer 8

yes. but I just noticed they are using 16 towns (not 12)

Answer 9

so 98.6

Answer 10

yes. in theory that is the number of people. so we either have 98 people or we say "roughly" 99 people

Answer 11

ok and Thank you so much again!!

Answer 12

and I guess you know we replace 16 with "n" to figure out the number for "n towns"

Answer 13

ok