Question

Brennan has been playing a game where he can create towns and help his empire expand. Each town he has allows him to create 1.15 times as many villagers as he had in the one before. The game gave Brennan five villages to start with. Explain to Brennan how to create an equation to predict the number of villagers in any specific town. Then show how to use your equation to solve for the number of villagers he can create to live in the 15th town. PLEASE HELP, I WILL GIVE BRAINLIEST!!

Answer 1

Answer with Step-by-step explanation:

We are given that:

Brennan has been playing a game where he can create towns and help his empire expand.

Brennan started with 5 villagers.

Each town he has allows him to create 1.15 times as many villagers.

i.e. after creating one town he gets 5×1.15 villagers

after creating 2 towns he gets  5×1.15×1.15 villagers

after creating 3 towns he gets  5×1.15×1.15×1.15 villagers

after creating n towns he gets $5*(1.15)^n villagers$

Hence, after creating 15 towns he gets $5*(1.15)^1 villagers$

                                                              ≈ 41 villagers

An equation to predict the number of villagers for any number of towns is:   Let number of towns be n

  Then number of villagers = $5*(1.15)^n$