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.

For each town he builds the number of villagers increase by 1.15 times.
So he has 5 villagers at the start, for the first village he builds he will have;
villagers = 5*1.15 = 5.75
For the next village = 5.75 * 1.15 = 6.6125
in other words for the second village in expanded form = 5 * 1.15 *1.15
as you can see the number of villagers keeps multiplying by the same factor thats 1.15.
For every town that is created, the number is multiplied by 1.15
theres an exponential increase in the number of villagers
Then we can build the following equation;
number of villagers in 15 towns = 5 * 1.15¹⁵
                                                  = 40.68 
 as its number of villagers it cannot be a decimal value therefore round it off to therefore we can use the following equation to find the number of villagers in 'n' number of towns;
villagers in 'n' number of towns = 5 * 1.15ⁿ

It would be 18 cm