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 as he had in the one before. The game gave Chase 4 villagers to start with. Explain to Chase 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 17th town.

Question

esha1963 · Answer

@darkknight

darkknight · Answer

This is very similar to the first question you asked help on. Can you tell me the useful info that they have given?

esha1963 · Answer

each town allows him to create 1.13 villagers more than the previous and 4 villagers to start with

esha1963 · Answer

1.13 times villagers^ sorry

esha1963 · Answer

and we have to create an equation and find villagers in his 17th town

darkknight · Answer

perfect, so 1.13 would be our slope and we would have a coordinate at (1,4)
I can see that this is different than the way that you have been doing but this is the method for algebra and it teaches you some useful formulas so lets do it this way:
So now we can set up our point-slope equation

darkknight · Answer

$$(y-4)=1.13(x-1)$$

darkknight · Answer

Distribute for x and solve for y. x in this case is the village number. And y is the number of villagers

darkknight · Answer

This equation would give you your equation in terms of villagers for the number of villages.

darkknight · Answer

How would you approach this?

esha1963 · Answer

can we do it the way how i did the first post? or that wouldn't work?

esha1963 · Answer

can we use t=1.13v?

darkknight · Answer

That would not work. Because you do not account for the y-intercept. we have to solve for our slope-intercept equation by first using point slope

esha1963 · Answer

where t is the # of towns and you solve for v?

esha1963 · Answer

oh okay

esha1963 · Answer

can we use the geometric series formula?

darkknight · Answer

So the way I have been doing it is correct. Your way might be a simplified version but the way I do it has a lot of algebra skills in it. Also the geometric series formula is to find the sum of all numbers leading up to it. So that is beside the point

darkknight · Answer

The way I have been doing it is pretty easy and simple. It also only uses basic algebra

esha1963 · Answer

okay can you teach me it your way? go through with me step by step?

darkknight · Answer

Yes, I already did. Read the above posts

esha1963 · Answer

so i would replace x with 17?

esha1963 · Answer

and solve for x?

darkknight · Answer

So the equation i got, do you understand how I got it?

darkknight · Answer

So you want to solve for y, and set the equation in terms of y. Just a slope intercept equation in the form of y=mx+b

esha1963 · Answer

yes you used the x,y coordinate

darkknight · Answer

$\color{#0cbb34}{\text{Originally Posted by}}$ @darkknight
$$(y-4)=1.13(x-1)$$
$\color{#0cbb34}{\text{End of Quote}}$
So that is the equation.
And we want to solve for y
y-4=1.13x-1.13                          Add 4 to both sides
y=1.13x + 2.87
Then plug in 17 for x

esha1963 · Answer

oooohhh. now i understand.

esha1963 · Answer

now that makes sense. thank you so much!

darkknight · Answer

Np

esha1963 · Answer

y would be 22.08 right?

darkknight · Answer

Yes, we can round down to 22 because we can't have .08th of a villager.

esha1963 · Answer

yes i was just about to say that lol

esha1963 · Answer

so 22 villagers in his 17th village

darkknight · Answer

Yeah

esha1963 · Answer

thanks!!

darkknight · Answer

np

esha1963 · Answer

i got this wrong :(  but the answer was
 an = 4(1.13)^n – 1 a17 = 4(1.13)^17 – 1 a17 = 28.269 28 villagers