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 as he had in the town before. The game gave Brian 8 villagers to start with. Explain to Brian 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 his 16th town.

Question

darkknight · Answer

basically, you will have an exponential function. since 1.17 times as many villagers as the town before, 1.17 is our base. Now the exponenetial formula is $$y= a \times b^t$$
Where we said that b (our base) is 1.17. Now it says we have 8 villagers to start with. So 8 is a. Now that you have your function you should make sure it is correct by plugging in values and seeing if they get back the correct answer

Kenley101 · Answer

Thank you!!!

Kenley101 · Answer

But then how do you do the second part where it is asking to find the number of villagers for the 16th town?

darkknight · Answer

So t is the village town number, can also call it x.
So you have $$y = a \times b^t$$
We know what a is and what b is. Plug in 16 for t. :)

Kenley101 · Answer

Ohhh ok thanks😁

darkknight · Answer

np bro. Click best response if u feel like I have helped. Have a good day

Kenley101 · Answer

👍