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 eight 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

I understand the question, I just need help with writing the equation...

Answer 2

let v be the number of villagers and t be the number of towns.
the number of villagers you can have is 8 times 1.17 times the number of towns

Answer 3

so 8(1.17t) = v?

Answer 4

i believe it's an exponential function. Because if you start with 8, and build 1 town, then you increase 8 by 1.17 times, but once you have a second time you increase the new amount by 1.17 times, right?

Answer 5

hmmm... ok... so 1.17(8t)?

Answer 6

my lesson is about geometric sequences if that helps.....

Answer 7

ok, so you need to tell us how long each "cycle" takes between the villagers increase. the equation so far is
initial villagers X (1.17 X Towns)^t

where t is how many cycles compounded once per cycle

Answer 8

i'm not familiar with geometric sequences

Answer 9

its ok @zimmah
@sylbot so there is an exponent in there?

Answer 10

i would say the 1.17 is compounding

Answer 11

ok

Answer 12

yes, it is because this is technically a differential equation, where the rate is determined by the function itself.

Answer 13

So the simplest way to explain it is, you need to account for the increase in people each cycle, that will impact how much it will increase the next cycle.

Answer 14

ok, makes sense, thank you both! :D

Answer 15

one more thing, you would need to modify that equation if they give you a certain amount of time, but if compounds more than once per cycle in that time.

Answer 16

ok :D