Brennan has been playing a game where he can create towns and his empire expand. each town he has allows him to create 1.15 times as many villagers. the game gave brennan 5 villagers to start with. brennan expand his empire by solving for how many villagers he can create with 15 towns. then explain to brennan how to create an equation to predict the number of villagers for any number of towns. show your work and use complete sentences.

The equation is an=a1(r)^(n-1)

A15= 5(1.15)^(15-1)

A15= 35.38

So about 35 villagers

You plug in a1 and the common ration to find the equation

an=5(1.15)^(n-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

Hence, after creating 15 towns he gets  

                                                               ≈ 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 =

what is the answer?

= 5

step-by-step explanation:

to find the 15th term substitute n = 15 into the nth term formula

= (- 3 × 15 ) + 50 = - 45 + 50 = 5