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. @imqwerty

Answer 1

Let ai= number of villagers when there are i towns.
Initially, there are a0=8 villagers.
a0=8a1=a0×1.17a2=a1×1.17=a0×1.172... ai=a0×1.17i

We need then number of villagers when there are i=16 towns.

Answer 2

he initially has 8 villagers
and the number of villagers will become 8(1.17) if he makes 1 town

if he makes 2 towns then the number of villagers will be 8(1.17)(1.17)
and like this

okay so let \(x\) be the number of towns
so number of villagers will be-
\(number~of~villagers=8(1.7)^x\)

Answer 3

so i do 8(1.7)(1.7) and so on then add them all up?

Answer 4

noo 8(1.17)(1.17) is the number of villagers when number of towns =2

well the number of villagers increase by 1.17 times when we make 1 town

originally we had 8 villagers so if we make 1 town the number of villagers become 8(1.17)

and if we make 1 more town i.e., 2 towns then the number of villagers become 8(1.17)(1.17)

Answer 5

we need to find number of villagers when number of towns =16

Answer 6

98.64

Answer 7

well the number of villagers can't be 96.64
so we must consider that the number of villagers =96

you might think that why we didn't consider it to be 97
thats because 97 is more than 96.64

Answer 8

alrightyy :)

Answer 9

:)