Chase has been playing a game where he can create towns and help his empire expand. Each town he has allows him to create 1.13 times as many villagers. The game gave Chase 4 villagers to start with. Help Chase expand his empire by solving for how many villagers he can create with 17 towns. Then explain to Chase how to create an equation to predict the number of villagers for any number of towns. Show your work and use complete sentences.
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
The number of villagers can be represented by y, while the number of towns can be represented by x.
So, Chase is able to create 1.13 times as many villagers. The equation can be turned into slope-intercept form, which is y = mx+ b. The only thing needed to do is plug them in.
Chase now wants to create 17 towns. Set the number of towns equal to 17 in the equation. He also has 4 villagers to start with. Now, the equation looks like this.
17 = 1.13(x + 4)
To find how many villagers Chase has when he was created 17 towns, create the inverse of the original function.